Don't bother fighting in the early going. Play diplotically. That said if you wind up next to the Saurians or the...Chryslons (cannot remember either's specific name for my life) on higher difficulty levels just start over. They will come after you right away and as the computer they cheat. So on anything but the lower difficulty levels they'll steam roll you right away. Even if you do win the war will cost you tremendously leaving you way behind the technology and exploration curve. Your best bet is to just diplomacy the shit out of everyone around you. Make them love you.
Research is key so don't slack off on it. The early game is all about keeping your research going full bore. You want to be able to build scouts and colony ships right away. Once you can start to build a half dozen to a dozen scouts and start to spam local space. When you find a world nearby with a promising planet (Very high in industrial production) colonize it. You'll want three or four colonies quick. Build five to ten transports as your colonists need to focus on building up industry, not farming. You need to keep your industry up at this time as well so you'll have plenty of cash. In the early going you can give yourself a huge jumpstart by using money to insta complete buildings. Especially the early ones like the Automated factory.
Keep steadily expanding your empire. Set up outposts everywhere. They'll extend your ships ranges and place provisional claims on star systems the computer is unlikely to contest. They also give you a bit of a boost when you establish a colony.
When you meet other races immediately start to woo them. Trade treaties are the easiest to get, and very profitable. They'll start them liking you. You can help yourself out by using those junk, non-military techs you get from creative as gifts. Things like biodomes will have little effect but could secure you treaties on down the line. Eventually start up a research treaty then go for the non-aggression. Once you've had that for a while and they really like you go for the Alliance. Alliances are pretty low key in MOO 2
, the AI won't really hold you to it, but you can use their outposts and bases, colonize their empty worlds, etc. The best part of an alliance is you can position your navy at all their major worlds, declare war, and decapitate them in one fell swoop. Yeah you're a bastard but hey, you won.
When it comes time to build your fleet design the ships yourself. I usually build lots of big battle wagons with energy weapons and point defense and then build hordes of small, fast, destroyer sized ships bristling with torps. The first turn, sometimes two is almost all battle wagons but then on turn two or three the destroyers get in short range and start unloading those torps at point blank. It's rare for battles to last much beyond the second turn of destoryers mixing it up. In fact small torp heavy ships are my favorites in the early going as they're relatively cheap and pretty effective.
"Tyyr's a necessary evil. " Spirit