Got a few hints that might help.
First of all, it's going to be a while before you have to worry about wars/ invasions. Planets can not be invaded without transports -- that requires Planetary Invasion tech and population to fill up the transports. Even on suicidal difficulty and Common settings for stars and planets -- and gigantic map with 9 opponents or huge map with 6 opponents or large map with 4 opponents -- war will not be declared on you till about 16 months into the game -- about 2 years if tough-crippling difficulty.
Next taxes-morale-population growth. Population growth is doubled if a planets morale is 100%; think it is 125% if morale is above 75% or 80%, not sure which.
Early on your tax income will be low so it is a good idea to lower taxes to get 100% morale on your planets and get your population growth doubled so that you'll have a larger population faster. Taxes = square root ( population in millions ) x Tax rate x Economy bonus's. Your going to need a population of around 6-7 billion/ planet to have a good economy and probably best to be in the 12-17 billion/planet range.
Spending should almost always be set to 100% if your not able to do this you probably need to work on your strategy.
Your going to be running an economy that is losing money every turn early on so I'ld keep some money in the bank early on, I'ld suggest trying to keep at least enough to finace 10 turns of deficit spending.
Usually it is best to buy a few improvements on your homeworld to get a jump start. I suggest getting the equivilant of 2 basic labs first and then 4 factories and then 1 entertainment network ( prob build this guy ).
I suggest getting Sensors tech at the start of the game and then researching to impulse drive with 100% spending and 100% research first. Then it is good to research Planetary Improvements ( +10% to social production, military production, and research ) and Space Militarization ( +10% military production).
If you are playing any of the update versions or betas, the anomalies will give money off and on. So it is a good idea to get survey ships early on. I buy 1 on each of my first 3 turns ( just a survey module and no engines ) -- use the pay over time option. Then i upgrade em with 3 impulse engines and 3 basic life support modules when i get impulse drive. Auto- survey if you like but i prefer to do it manually and out manuver the AI to the anomalies.
Once you get impulse drive you can design a colony ship with 2 impulse engines and 2 basic life support modules -- this'll give you both speed and range. I like to set my military spending so that i crank out a colony ship every 2 turns off my homeworld and set the rest to research with social spending set to zero. I like to buy labs and factories on 300% bonus tiles -- 100% bonus tiles if i got a lot of extra money ( but prob best not too, the deficits get pretty large ).
Personally I like to buy a starport on each world as I colonize it and leave building factories, labs and market centers till I'm done colonizing and then do all my planets at the same time. But lots of players like to buy/build a factory first. I also put off doing upgrades to factory, labs, and market center techs till I've built them on my planets. Also I put off espionage till I'm done building the basic buildings -- nothing like getting an upgraded tech that requires you to build a more expensive building-- to ruin your day. I build the equivilant of at least 3 factories on each world, labs on research bonus tiles and my tech capital world ( or what will be ), market centers on rest of tiles except maybe a farm or 2 per world.
Don't forget to use constructors to make starbases on the resources as you can. The AI isn't the best at claiming them -- if you get a few constructors with good movement you might even get some on the far side of the map. I don't much care for the influence resources but the morale, military, and economic resources are all fantastic -- the research resource is just good but definitely worth grabbing.
As far as what to research during this phase -- depends on your style -- i like to go to warp drive pretty fast and like to get to Xeno Entertainment for the +10% morale bonus. You'll need to pick up some techs that give diplomacy bonus's if you plan on doing much tech trading. And going for the Goverment upgrades will give nice bonus's too. Also you'll need to get the techs for the different hulls to build military ships. You'll need weapon techs to put weapons on your ships -- they are all good -- i like missiles myself -- a lot players seem to like beams -- and a few like mass drivers.
After factories are in, the factory tech upgrade tree is one of the first to concentrate on -- besides factory upgrades you get starbase module upgrades to get even more benefit from mining resources. And get constuctors out to the mining starbases to upgrade em -- fully upgraded they give civ wide 44% bonus's.
A neutral alignment will allow you to make all the tiles usuable which require terraforming ( any of the 3 processes ) -- just by getting Xeno Ethics tech. So choose neutral on planetary choices when colonizing or it'll cost a lot to choose a neutral alignment and get this bonus -- also get the Neutarlity Learning tech on tech tree with neutral alignement.
Miniaturization techs give you more space on your ships so you can put more weapons and engines on em usually. See posts on "Miniaturization Bug" if you want more detail info -- not going to get into that here other than adding that " usually". hehehe!
Engine techs -- always nice-- faster ships equates to picking your battles.
Logistics techs are needed to put more ships into a fleet.
Sensor techs give you better sensors and last sensor tech gives the ability to build the "Eyes of the Universe" galactic achievement which a lot of players swear by and i do it occassionally myself.
Life support techs give more range to your ships -- usually not much of an issue and you'll probably not have any life support modules on most of your ships -- but very nice for long trade routes if your going to use trade.
Defensive techs -- i don't bother and don't do any defense on my ships -- but lots of players swear by em.
Hull techs not only let you make larger and larger hulled ships but give your ships HP bonus's. Also there is a line of weapon modules for your starbases.
Morale building tech give morale bonus's for the tech which is nice but not crucial.
Diplomacy techs give diplomacy bonus's which are nice for dealing with the other civs.
Trade techs let you build more trade routes -- i don't bother with trade routes and have a very good economy without em. But lots of players swear by trade routes which also make for better relations with your neighbors.
Market Center upgrade techs -- everyone goes to Galactic Stock Exchanges as best they can -- stock exchanges give +30% economy, +10% morale, and +5% influence bonus's.
Farm Tech upgrades -- i like 1 tech upgrade -- usually just trade for it -- but lots of playable options -- you need farms but not the biggest deal in the game.
Research building upgrades -- nice -- do em as you can -- the NLCs for neutral alignment kick ass.
As to when to start building ships -- watch what the other civs are up to-- you can wait for a little bit after they start building but not forever. If your military rating is high enough they will leave you alone. The stats and graph page of your civilization manager has a feature where you can compare your civ to the other civs one by one to see how your doing. Also the relations page of the foreign policy screen will show you how the other civs feel towards you -- if they get wary be prepared.
As to ship design, depends on your play style -- they'll all work if you design em well -- definitely design all your ships. See what kind of ships your potential enemies have and design to take em on. I like ships with lots of speed and moderate weapons. I prefer largest hull i can make -- but lots of players like small hulls.