I've only played one game of GalCiv II to completion, but I've got a lot of Galciv I under my belt. My stragety has generally been to decide on a strategy (conquest, tech victory, alliance victory, etc...) and focus my research on those areas, but when an otherwise useful tech (say - sensors) comes available and can be researched in 2 or 3 turns, I go ahead and get it. You can often trade techs with your friends and you should. You can also make a fortune selling tech to the independent worlds. I would always sell them all of my tech just before conquering them, just to be sure I got their money too.
Also of note: techs that make your population grow are important to any strategy. Population is the engine for any of these strategies. Also, you will need to at least remain competitive militarily, so you can't ignore your military altogether.
Good Luck!