I have played all of the races in TA, and one thing applies to them all, and it is precisely what Piznit said: Focus on economy. It is much more difficult now to grow and maintain a robust economy. (As you know) Here are a few things that I have learned along the way, that apply to any of the races.
1) When making your racial picks, pick economy, pop growth, and morale. These have been the standard picks for awhile, and are even more useful now. You don't *have* to pick this way; in fact I mix up my picks quite a bit from game to game, but it will make life easier later on. Creativity is the best 1 point you can spend, though. There is nothing like seeing a 52 week tech proc in two.
2) Grow your population as quickly as possible. It takes taxpaying citizens to fund your projects. Build recruiting centers asap, and try to keep your approval at 100%, in order to get the 100% pop growth bonus. You will probably have to lower taxes, and/or build a morale structure. At the very least, try to keep your morale above 75%, so you will get the 25% pop bonus.
3) Be very judicious about building social projects. I spend a fair amount of time early in my games building nothing at all. I usually build a recruiting center, an economic structure, and perhaps a morale structure, if necessary. You can build a basic factory, or lab, but again, go slow. Avoid building on bonus production or research tiles at first- the extra production comes with extra cost. Wait until you can afford to build there.
4) Don't expand too quickly. This will break the bank faster than anything. Of course you will need to expand, just be smart about it. Take only the better planets (for the inherent morale bonus) whenever possible. And when you do, get their pop up asap, so they will begin paying for themselves.
5) Don't build up a grand fleet right away. Maintenance costs on ships are high. At first, all you really need is a defender or two in order to keep the AI off of your back. Survey ships can be one of your biggest advantages, though. If you have few anomalies in your game, then stick to the one you are given, but put it to work right away. If you have many of them, build 2 or 3 more, and snap them up. When those 1000 bc amounts come rolling in, you'll thank me. Those alone can give you a lot of leeway in how you grow your civ, and all of the other bonuses can really add up as well.
These are just generalities, to be used, modified, or discarded, as you see fit. In the game, as in real life, you have to live within your means. Remember, the AI is playing the same game you are, and faces the same economic conditions. (At most difficulty levels.)
Hope this can be of some help. Good luck.