BotF is one of the worst 3X games for the computer players running amok at higher difficulty levels. MOO2 has nothing on it. Because you don't get an automatic advantage for being able to design your own ships, you have to be very careful, and avoid war until you get decent tech and build up your fleet a bit.
It helps MASSIVELY to be able to get a few good neutral races on your side: they have ships and well developed planets. So you need to explore heavily and try to find those, while you still can. On the other hand, the longer you can avoid running into hostile computer players (or, god help you, the Borg) the better.
One of the things that really killed the popularity of BotF was the fact that you could have random Borg at like turn 20, and there wasn't a damn thing you could do about it...They could walk over your whole empire without even blinking.
Other than that, specialize your planets, keep an eye on your economy, and try not to get in any wars that you can't win. Generally you need your first planet to be all industry, and subsequent planets to push research. Churn out scouts, and upgrade your buildings whenever you have the opportunity.