Well, I'm not playing the game on an insanely difficult level, but with one Dumb AI (or whatever is one step lower than normal), two Bright AI's, and two normal AI's, I'm not having too many problems keeping up. I am approximately the same in population as the strongest enemy, way ahead in tech, and a little behind in military.
Here's some of what I do:
- Use at least 3 of your advantage points on population growth. It's really important to have extra population, and those 3 points are pretty much worth 3 points in almost every other category because of increased production.
- Don't build a colony ship on credit. Your first planet should start building a colony ship right away, while you set your surveyor out to collect materials. Use him to scout a little too. Increase the tax rate and military spending to get the colony ship completed in a timely fashion. You can slack on research for a little while.
- Try and find planets that will likely be out of range of any enemies. You can save those for later. You only need to be quick to colonize the planets that will border an enemy civilization. And even then, only really the ones that are 17 quality or better. No sense rushing to take over a planet that will only be a minor benefit to your empire. And it's hard work to keep 15-quality planets happy. Usually, I only need 2 or 3 colony ships quickly, although I basically keep my home planet constantly making colony ships.
- Start building a constructor at every new planet (unless it needs defense right away, which it usually won't)... even if you need to switch production later, at least you've saved up all those turns of building. After a few years, you'll start to be surprised by the number of constructors you've got popping out.
- I usually put a point or two into speed, and research at least the first speed upgrade. Colony ships and constructors are godawful slow, and you may lose planets and resources if you can't get their fast enough.
- Trade all of your tech away to minor races. All of the minor races. Make sure to trade with all minor civs on the same turn. Try to get a large amount of BC for 40 turns. It doesn't hurt to have a point or two in diplomacy, or to research the diplomacy upgrades. I run most of my economy on tribute, since my research is ahead of the rest of the galaxy.