Everyone has a different formula. Here's what works for me....
Phase I: The land-grab.
Set your research (whatever you want). I usually go for the ones that improve my economy first, like planetary improvements, or something with a diplomacy bonus).
Set your tax rate to as high as you can go and keep your overall approval rate at about 50%. Don't worry, the colonists can't vote yet, so you won't get overthrown. Since you are buying your ships right now, and research isn't all that critical the first few turns, put social procuction to 40% and the others at whatever suits you.
I pump out colony ships one-per turn until I am out of money. Get the good worlds. If the AI takes a cheesy little planet (MARS) it will eventually defect to your superior culture. It is real important, though, that you don't get too many quality alien planets within your borders.
Phase II: Social projects
The Idea here is to build your economy. You will probably need to tone down social production a little, but it should still be a priority over research and military spending. Keep making colony ships until there aren't any more planets to get. When there aren't, convert your colony ships to constructors. The first few things to build on any good planet are a couple of factories and a starport. Low quality colonies you should specialize in something. I prefer using them for research worlds. Once no more planets are available for colonization, switch all of your starports to make constructors. Grab every resource in your territory, then any outside your territory that you know of. Keep pumping the constructors out until you have defended all of your resource starbases with three upgrades: (Basic weapons (+1 each type), the +7 beam one, and the +5 defense of your choice). Once you've done that then strategically choose to upgrade the mining to get what you need. During this time, you will want to start down a weapons branch of research and get to the top of a first tier (Lasers V, the top miniballs, the top stingers). I don't mess with engines or defenses yet, because my first ships are defense-only anyway. Once you have a design, switch about 1/2 of your starports to make these ships. Your first goal should be to get one in orbit over all of your planets, then eventually 2 or 3 at every planet and starbase. I also like (although this is not required) to make a probe (just a hull with sensors) and put a bunch of them around my 'borders' and even park one near all of the planets outside of my borders. It sure is nice to know when the Drengin are emassing a fleet of transports. Alternatively, if they aren't being too sneaky about it you can take a hint that thngs are about to get violent when your probes stop responding. After your resource starbases are topped off, build some economic and military bases. At this point, only mess with influence bases if you are in danger of losing a colony to an alien. Oh, I forgot trade route. You have to get them up and running, and fast, and especially with the bullies. That will make them leave you alone and pick on someone else for a while (hopefull). If someone does declare war on you you should be able to hold your own. You might have to research invasion, and you might have to switch some constructor production to your fighters, and build more military bases than economy. Basically everyone is wimpy at this stage, so just send a few task forces out to blow up the other guy's starbases and then camp his planets with a fleet of fighters so as soon as he builds something you shoot them down one-by-one. Don't worry about crushing them right now. The ones not involved in the fight will overtake you developmentally and you'll be in trouble later. Research should more or less be completed on the cheaper non-military techs in trade, diplomacy, and production. Of course, get the research upgrades first, so the rest of the research goes faster.
Phase III: Choose you win strategy
By now you are sitting pretty. You probably have the best economy in the game, your research is way ahead, your military is at least competitive. If your lucky eveyone else is at war with someone. If one alien starts losing to another pay it a visit and give it some juicy weapons tech, a few ships, or some cash to help balance the scales. You want them to all stay in a destablized state. If one gets the upper hand, you'll be next. Now is the time to research your way further up the weapons tree, the defense tree, the engines tree, miniturization, and fleet size. Once you have some goodies, build your first medium range corvette class ship. You want something that you COULD use to whack an alien if you wanted to, so the no-engine fighter won't really do. Crank out about 6 transports too, even if you don't need them right now. At this point, you can take your pick- Build up an awesome military and take out your enemies one-by-one (starting with the minors), carry a big stick but build influence bases like crazy and go for the cultural victory, or carry a really big stick and go for the long and lonesome tech win. This part of the game is a lot more unpredictable, but the key is to keep those aliens killling each other instead of you. Again, when one starts losing throw it a bone. Oh, be sure to ally yourself with aliens you usually get along with. I like the Alatarans and Torians because they generally aren't treacherous. Just watch out for the Altarans, as they will build influence bases right next to your homeworld and start distributing porn to all of your kids.
That's my formula. It usually gets me an influence win, although I could go with just about any type I suppose.