I've only been playing for a couple of months, but I have developed a starting strategy that works pretty well for me. I've gotten through painful, but have not yet won on crippling.
I'm usually the Altarians with additional economic, morale, and research bonuses on top of their racial abilities. Sometimes I'll put a lot of the optional bonus points towards speed. I also prefer larger galaxies and lots of everything.
1st turn: If I can, I'll design a colony ship with a small hull. On my HW, I'll buy a factory and start building a second. I'll start construction of the cheapest colony ship I've got and set focus to military production. I'll set my sliders for 100% production and leave the others at 33/33/34. I'll adjust my tax rate to maximize income while maintaining 100% approval (easy with Altarians). I also try to remember to order my initial colony ship back to my HW to pick up more people.
On my HW, I'll buy factories the first few turns to speed up production of colony ships. After that, I'll build some labs to boost research.
Although I prefer to specialize planets, I start off with a balance. I start with at least two factories on each planet and, depending on financial situation, I'll usually buy the first one. I also build a star port on the first few planets. I take advantage of the high pop on my HW to help my fledgling economy with at least three markets.
I rely on my HW to produce colony ships and my first few additional planets to produce survey ships (I will have researched sensors by this point) and constructors. If I find a juicy PQ16+ early on, I'll make it an economy world after plopping down the standard pair of factories.
In general, I make most PQ16+ worlds focus on economy, and after the two factories, I go crazy with the markets. When the population nears maximum, I'll build a farm and eventually a moral building. With the Altarians, I end up with two farms and one moral building on each econ world. The rest are econ buildings and one will typically become the econ capital.
Once I get a few econ worlds, I'll start specializing the PQ15- worlds. If they have a moon orbiting them, they usually wind up becoming production worlds and get a star port. The other PQ15- become research worlds and get nothing but two factories, lots of labs, and often a farm. Every planet, once they become PQ12+, gets a farm. If I get enough PQ16+ worlds, I'll dedicate some of them to production or research. Bonus tiles also help decide which way a planet will go, and one or two planets may do both production and research if they have the right tiles. I also try to make it so that all research and economy worlds are within a reasonable distance of a production world since they don't have star ports of their own.
I do get the early warfare techs pretty quickly, but I don't research any particular weapons or defenses until other races start militarizing. I concentrate on economics, diplomacy, research, and planetary improvement type techs as much as possible, but I will take the time to research advanced colonization techs if the situation calls for it. If you're in the vicinity of the Korath, make sensors a big priority and keep an eye out for their spore ships.
I'm an expansionist and prefer to live in peace with my neighbors. I like to groom all of my worlds and keep them well manicured. I try to maximize trade and if my financial situation looks good, I'll lavish the more powerful races with gifts. I'll make sure to keep up militarily so the more aggressive races don't get any ideas. And if they do, they usually wind up paying dearly for their mistake.
Don't overlook those little PQ1 worlds. They become monsters after a little terraforming. Also be smart about your planetary improvements. Don't upgrade your factories until your economy can support the increased production and don't upgrade your research facilities until you have the adequate production to produce the better labs in a reasonable amount of time. Unless your economy is very strong, avoid having all three planetary types (econ, production, research) upgrade at the same time.
Always be thinking about your economy, always.
Well I think I may have gotten a little carried away, but there you have it.