Game Setup

Obviously this is going to be a personal preference but I like to have it set to abundant everything on a gigantic map. Star density set to tight clusters and a tech rate set to very slow. You can make a custom race which is what I prefer.
Set planet quality to +20%,
population growth to +20%,
federalist party.
For the initial techs you can choose which ones you want your race to have.
I choose:
Hyperdrive
New propultion Techniques
Ion Drive
Galactic Warfare (+10 ship building)
Space Militarization (+10 ship building)

First Turn

-buy a factory on your main planet
-Queue up three or four more factories (or the equivalent with tile bonuses)
-go into ship designer and design the fastest colony ship you can make with your new engines
-set your homeworld focus to military production
-set taxes as high as you can without dropping your approving rating below 45% (If happiness in the red there is no population growth, if in yellow = normal growth, green = +20%, 100% happy = double growth.
-set industrial capacity to 100%
-set sliders to about 40-50% military, 8-12% social, 40-50% research (It varies turn to turn)
-SAVE GAME!
-set flagship to auto survey
-use a ship (scout or the initial colony ship that you get) to explore nearby systems. Make a small map for yourself on paper. Continue this for as much of the galactic map as you want.
-RELOAD GAME! (I realize most people consider this really cheesey but I insist to those people that the computer knows the map already. I've seen the computer go right for the largest planet in a solar system then send other colony ships even farther out before settling a smaller planet in that system, so it knows where to go! Besides the save game at the begining gives the AI a free turn, every time you save/reload the AI gets a free turn of production)
-send your colony ship to the nearest but largest planet.

Colonization Phase

Within the first couple of turns you should be able to make your first fast colony ship. You can do this in five to six turns if you've continued to buy a couple of factories on your capital. This negates the need to buy them, as it is disadvantageous to do so for population reasons as well as economic ones. Any planet over 15 PQ I make into an economy planet. Usually my build queue is Fac, starport, lab, fac, lab, fac and then all labs untill I hit the population limit and I add a farm. On econ planets I'll start with the first 4 then just make money tiles until I've built the whole planet then convert the 2 initial factories to econ tiles too (besides something got to pay for the infrastructure I'm building).
Science in the colonization phase
There are a couple of things at this stage that are crucial to remember. Military production is production for ships, so increasing military production early on helps make colony ships. The faster you can expand the better. So for some of the initial techs I choose galactic warfare and space militarization, both of which gives +10% military production. I then research xeno egnineering (+10% social production) then planetary improvements (+10% military, social and research). I usually research impulse speed next. I immediately design faster colony ship. I cannot overstate the importance of fast ships.
At this point my colonies are off to a decent start and I research xeno research, advanced computing and basic miniaturization. Miniaturization gives your ships more room for components (engines, weapons and defence). Usually I builds labs in every tile free after factories and basic entertainment/farms (if I even make those), that doesn't have a bonus for something else, if it has a research bonus that is the first research tile I develop. On a larger map I then get stellar cartography and sensors to make more survey ships (I play with lots of anomolies) I then go for the trade advancement; xeno communication, universal translator, diplomatic relations, trade. I get trade for two reasons. Not only does it give great bonus' (trade, diplomacy +10 and +3 trade routes), but it also gives two great improvements, the restaurant of eternity (which improves your influence by 20%) and the economic capital which doubles the taxes taken from a planet. Then I go for xeno industrial theory for the manufacturing capital which it also gives you better factories (at a higher cost of course).
At this point your colonies' populations should be getting fairly high so watch your happiness and adjust your taxes accordingly. If you have a fair amount of money still (which is a possibility), you can drop taxes so that each system is at 100% happiness to get a double population growth bonus. The next thing I go for is Xeno Ethics. It has a huge effect on the game. As you go through the game you have had the option to to do the good, neutral, or evil things, with bonuses or penalties. These decisions also determine how the other races interact with you. After xeno ethics you've choosen once and for all. Each of the choices also give some amazing bonuses. If you choose good; you get a special temple and you get to research some of the best defences in the game. If you choose evil you get a temple and some of the best weapons in the game. But in my opinion neutral is the best. You get a temple, morale boost, and better trade. The best thing about neutral, however, is that all of the yellow, orange and red tiles automatically get terraformed. That's a lot of tiles instantly converted for you! The other thing that rocks is, whether you are a heavy researcher or not, it gives you the neutrality research center. These give amazing research. Once you have a good research base, you can concentrate on your economy. Research the xeno economics branch to the end to get the stock exchanges. These give a 10% morale boost, a 30% econimic boost and a 5% influence boost all for 1 bc maintenance.
In hard games, after Xeno ethics, I research planetary invasion and the soldering techs. There are two reasons for this. Either there is a close agressive AI that's already attacking you. Or an AI race is way ahead of you in one or more branches of the tech tree. Against those races you need to strike preemptively. With a good soldiering ability your troops will be better able to repel an attack or take undefended systems from a quickly advancing enemy. I usually play on very slow tech games yet this should only take 60-70 turns to get to planetary invasion.

Mid Game

Mid game I define as after you've colonized all that's practical to colonize (planet quality fours and fives only get colonized last). By this point you do need a basic military (if not sooner). I've calculated how many research points it takes to get to the end of each branch of the weapons branches. The beam weapons by far take the least research to complete at 49,125 and since those points are spread over more techs you get to more advanced (read smaller) weapons sooner. Mass drivers (guns) come in second with 64,975 and missles come in last with 74,250. Mass drivers, however, are much more efficient in size/damage on your ships throughout most of the game. My preference is mass drivers overall. The early advantage to missles is that the first true missle that you get is a damage 2 weapon, whereas the other ones take a couple of techs to get to a 2 damage one.
One thing the computer tends to do is colonize a small planet in a system you control and build influence improvements. This helps their economy through tourism. This is also a strategy to consider as well against a more passive AI player.
Here it's definately about micromanagement to be effective. Continue to build farms on systems as they near the population cap and entertainment to keep everyone relatively happy. It's usually a two to one ratio of entertainment to farms, unless you've made the galactic wonders of happiness crystals(+20% happiness), ultra spices (+15%) and frictionless clothing (+12%), virtual reality modules (+10%). With a couple of morale resources amxed out you don't even need morale building on your planets, just the galactic wonders!! As you start to develop some of your large planets, make sure you can balance the budget (if not start making money). You may have to upgrade some of your neutrality learning centers to stock exchanges on some planets for the economic bonus. The goal should be not to make every planet into a money making machine but to have a couple of your largest ones into money planets. Maximize the return on your largest planet by having just farms and stock exchanges (these planets start as a regular system of a couple of factories and then as it grows you upgrade your factories and labs to stock exchanges and farms and perhaps an entertainment center). Also make your largest and best developed into your economic capital and build freighters up to your maximum number of trade routes, then build four economic starbases with the trade bonus maxed out. On any system over ten (even money planets) always have a starport, because you'll need those ships eventually, even if you're just making constructors. As you grapple with your first (or second or third) rival you eventually have to decide how you want to win it.
Science in the mid game
After I start the first war against the AI I usually go for xeno entertainment and extreme entertainment to make ultra spices. I mix in some weapons techs as I need. I also go for research centers, acadamies then neutrality research centers. Usually my economy is a bit stretched at this point so I go for zero G sports and virtual reality center (to get the virtual reality module). This alows me to raise tax rates to increase the money coming in. I also mix in logistics and miniaturization as needed but I rarely get anything beyond advanced hulls (unless I steal it). I sometimes add larger ships to a fleet but rarely do I research it on harder games. I usually work on xeno business, cultural domination, historical assimilation, and xeno cultural trends. I do it for 2 reasons. I'm usually building influence starbases on the passive players and I also get frictionless clothing. If I can spare the turns I also get a better government to get more money.

End Game

Pursuing an overall end game strategy can be daunting with 250 plantets all needing their own attention. Once your economy is going fairly well it might be a good idea to lower your tax rate to keep people happy. If you've made some or all of the morale wonders you may be able to even raise taxes and make more money. Remember to build economic starbases around your manufacturing centers with 4-5% bonus per consructor to military, social production and research, these can make a big difference.
If you're going for a tech win, make just enough money planets to balance your economy and put everything into research. Reasearch to the end of the diplomatic branch (advanced diplomacy, expert diplomacy, majesty, total majesty) to get the spin control center. It increases the military rating on the planet it is built on. So make some large or huge hulls with as many of the most advanced weapons you have and leave them at that planet. Your military rating will sky rocket and keep the enemy off the offensive (usually). It's a cheap way (resource wise) to keep the enemy away.
If you want to go for an influence win, build many influence starbases especially on the military power next to you (and do the above spin control center trick). Make sure when you're building your starbases in enemy territory that you send five or six (or 15) constructors and max out the base at once (including offence/defence). I tend to have six or seven groups of ten, make upgraded starbases all in the same turn next to one races maxed out planets, and then laugh maniacally. As you may have noticed in your previous games, the more influence you have the more tourist income you get on your planets. It can be a decent money making venture to increase influence, you may be able to offset a large portion of your taxes and keep people very happy by lowering rates. I've been able to flip 8 planets in a handfull of turns using this strategy against the Korx .
If you plan to go for military conquest you need to balance the need of research with a great economy (to handle the cost of all those ships). The way to combat huge maintenance costs are to not have them. Have most of your ships on the front line. Be on the offence as much as possible. Make extreamly fast troop transports. This is for two reasons. You can out manouever the enemy which is the best way to handle troop transports. Diplomatic victories are in some way the easiest and in some ways the hardest. If you're neutral (which I recommend) and the galaxy is divided between good and evil, both sides are distrustful of you. It can be either tricky diplomatically and/or expensive to end up in a large alliance. What usually ends up happening is there is one or two who end up declaring war when you start to get close and are usually more militaristic than you. The trick is to not try to get an alliance with them. Do the spin control center trick to keep them off balance. Build infuence bases all over thier territory and go on the offensive militarily. Send in a small fleet to each of their eight to ten largest systems followed right behind with troop transports. When you do end up attacking, always come from mutiple directions and go after different objectives, keeping the enemy off balance. The idea is to hit so hard and often that the enemy doesn't do anything to counter for fear of losing something greater. The AI in this game is good and I've seen it make some great strategic moves, but it can't handle ten to twelve fleets attacking different systems, getting ever so much closer to the home system. Heck I don't know if I can handle defending against that kind of offensive. Rember though in the end game once you've chosen your victory method to maximize the resources for it. A rule of thumb; Happy people pay high taxes, lot's of people pay lot's of taxes, unless they're miserable.

Battles and Ship Designs

I haven't talked a lot about battles in particular yet so I'll devote a section to just to ship designs and battles. If you are ahead technologically it can be easy to assume you will win easily. Do not make that mistake! There are a lot of ways to beat a more advanced enemy. If the enemy is making large powerful ships, get basic logistics, a good weapon, and make cheap tiny ships. Put them in large fleets. Attrition can be high, but if ony one tiny ship dies and you kill a large or huge ship, who's winning in the end? You guessed it, you are! Take out as many vulnerable colonies and then force peace. If the enemy is doing everything right (small or tiny ships in large fleets) there is one way not to get destroyed, don't engage them. Build extreamly fast ships and out-manouver them. When we get tactical battles in this game like and oldie-but-a-goodie Birth Of The Federation ship designs will have to change to reflect the dynamics of the new battle system, but for now it more about speed, logistics and the most important thing, miniaturization. If you are more advanced than the enemy, then you do have more options, but you have to worry about resource management and having an effective military, not just a larger one. I usually have one large or huge hull with a bit of defence but lots of the best weapons (for their size, meaning power divided by size) in a fleet with lots of small or tiny ships for cover. The computer attacks the ship with the highest threat first and that is calculated by attack divided by (defense + hit points). So small or tiny ships are often the bigger threat even though the larger ship does the majority of the damage. You can calculate which ship will be attacked first based on this simple equation. You may also want to do the opposite at times. If you're way ahead or have a wicked defence against the enemies chosen offence, You could make a huge ship with just enough defence to keep it alive and lots of offense and make tiny ships that'll never get touched and never waste reasources. That's unlikely, you will have to make a decision on what's acceptable losses eventually. If I am behind technologically I do end up taking slightly greater loss in favour of good weapons until I catch up or surpass the immediate enemy. Always concentrate on the immediate threat. Don't tailor your current ships to an enemy that you may have to fight in fourty turns, worry about the Drengins attacking this turn. A note on defence. If you have the right defence for the type of attack, your defence is calculated directly one to one. If you do not have the right defence for their offence however you aren't completely vulnerable. If you have sixteen armour defence and the enemy is attacking with missles, you still have defense (which does make sense if you think about it). Your defence rating however is the square root of the wrong defences pluse the right one. So for example you have 16 armour and 16 shields and being attacked with beam weapons, you end up with 20 defence, 16 + (square root of 16 is 4) = 20. It can be advantageous to research a defence that the enemy isn't currently using. For example, a good defense that takes little room on a ship can help even if it's not the right type, or if you research to the end of the point defence branch you can make hyper computers (+20% research), which is a huge tech to get! Just for reference sake to get to the end of each branch of the defence branches; shields cost 16650, armour cost 16650 and point defence (and hyper computers) cost 12220. If the enemy hasn't started making highly armed ships (or you're playing on a gigantic map and haven't seen the enemy battleships yet) you may just want to push for the aeron missle defence at the end of the point defense branch to get those hyper computers.

Economic Strategies

The money your civ takes in is calculated pretty simply. It is your population times your tax rate, with bonuses or penalties based on your government and resources, plus your trade and tourism. So one thing that is important is increase your population as quickly as possible and keep people happy to keep tax rates high. Ususally as I near the end of my colonization phase and I'm losing a fair amount of money per turn. Before I go broke, I drop taxes significantly to make people happy. This increases the pop growth and when I move my taxes up again, I'm making more money. It's kind of hard to think that dropping taxes can result in more money later but it's a fact! I then look to get morale resources and build the happiness wonders. I often make just one farm per planet, occasionally 2, and build lots of stock exchanges. I shoot for planets to have 15-18 billion people on them.