I agree with Mystikmind for the most part. I wouldn't say "never" to anything, but it's pretty close to never as far as building galactic structures on good planets, unless there's a compelling reason for doing so.
Mystikmind's focus on economy sounds right on target too. The economy will make you or break you.
I play suicidal on small galaxies right now, because I don't have time for larger ones ATM. I might go with a larger one after my vacation. Maybe.
For the below line by line comments, I play either all factories or all labs strategies, which is a little misleading. (Most of my structures are economic.) If I see a real good research bonus on my homeworld, I'll go with all labs for the production and set my sliders to 0/0/100. If it's a tie or social looks better, I go with all factories for my production and sliders go to 10/90/0. (I don't like the more expensive 1/99/0 settings, but that's just me). I adjust focus on a turn by turn basis, using the governor screen.
1). For my homeworld, I go full production. Rush buy labs or factories, depending on the chosen strategy. One farm when it looks like it might need it. If I can get a manufacturing or research capital, I'll build or buy that when its bonus outweighs the basic production unit. For new colonies, I build two production units one economy, a starport, then all economy, save one. That last one will be a farm, unless the planet needs one sooner. Only one farm per planet and not on a bonus tile. If I come across a planet with appropriate bonus tiles, I'll use it as a full production planet. I used to buy entertainment buildings, but found them to be relatively useless for my purposes. The exception is when I conquer a planet that already has an economic capital, some other morale boosting structure and a bonus tile for entertainment. In that case, I'll build one and also put two or three farms, until the approval goes way south.
The reason for the stardock on every planet comes into play when I build my "lure", which starts as the colony rush is ending. The planets supply it with fighters and constructors. The lure is a military starbase with every ship assistance module that I can get, focusing on attack first. It'll be close to my initial border, close to an intersection of 4 sectors and its range will encompass at least one lower class planet. (The low class planet doesn't have to be mine yet. I'll have it soon enough.) I surround this starbase with 1 weapon tiny fighters at first. By the time there are two fighters in the 8 squares around the starbase, I'll have enough miniaturization to uprade them to 1 attack and one defense. The lure is almost always attacked by the first aggressive AI on one of its corners. I beef up the corner that faces the most likely aggressor with 3 or more tiny fighters. The lure eats up anything that attacks it and keeps the less aggressive AIs from wanting to start anything. Eventually, the lure will grow to 8 or more starbases. It'll give its assitance to the low class planet when I eventually put a Spin Control Center on it and fill it with Huge 1 defense, no engines, balance attack ships. That gives me the ability later on to decide when I want to go to war and lets me build influence starbases or set troop transports wherever I want with relative impunity.
2). I build my own colony ships. Cargo hulls, one colony mod with two or three engines, one or two support and send them out blind. I grab as many higher class planets as I can until my economy starts to tank. Sometimes, higher class only means 8+. Usually, it's 10+. The lower class planets in my influence area will be colonized by an AI and will flip to my side after the AI builds them up for me. I use an extra colony ship to ferry colonists from my more populated planets to the lower pops, upgrading its engines as I go. That lets me raise taxes while keeping the growing colonies at 100% approval. I build up the planets close to any AI planets that I want to flip first. More pop means more influence as well as more money.
3). Research for me depends on the feel of the game, my race and how close my neighbors are. I generally go for some diplomacy, engines unless the colony rush looks like it's ending, morale, more diplomacy, influence and then production (research for all labs or social for all factories). I trade for my military techs, but will research some of the starbase techs myself.
Tech trading is the major part of my games. By selling everything except diplo, I stay solvent and also keep that money out of the AI's hands. It really bothers me to see an AI with over 1000bc. I see that as MY money.
When trading, remember that the AI values single items in trade over multiple ones. If you want, say, Warp Drive II, but the AI won't trade, try asking for Warp Drive I AND Warp Drive II. I've had that work for me so many times. Also, ask for 1 influence point before asking for money or tech. That devalues the AI's side and increases your bargaining power. If not 1 influence, remember to try to ask for multiple things for your one thing. You'll come out ahead in the long term, even with lower diplo skills.
If the AI has relatively nothing to offer and you want to bog him down with a trojan horse (say you want to give him Ultimate Invulnerability to bog down his military), ask for a troop transport. That'll give you 1000 colonists to boost your economy while you unload the tech. A double whammy on your part.
Don't trade away soldiering skills if you can help it. Advanced Troop Modules is OK, but not Plantary Defenses. You want as many of those for yourself as you can.
Before you completely conquer an AI, trade the rest of your techs and drain him of money and influence points. He won't be able to trade them away and it helps your economy. If you plan on letting him live through a turn, consider offering peace in exchange for a planet or two. That's more important if your alignment is something other than neutral, since he's likely to surrender to someone else.