My usual strategy until now's always been to rush my colony ships every turn at the start and send them every which way in the hope of finding a planet. I usually play on a medium map and find that if I don't do this, the AI grabs all the planets before I can.
This is a good idea if you're playing a medium map against all 9 opponents. Only if there are more than a few planets to colonize, you're better off buying or building the factories and building the colony ships because it's much cheaper.
Once I've colonized all I can, I'll usually go after a few economic techs, mixed in with the manufacturing techs to build up my industry.
Make sure you're trading for techs whenever you can. The AIs trade amongst themselves and will pull ahead of you if you don't trade, too. On the other hand, you can trade much more effectively than them, and use that to keep up in tech for cheap.
At this point, I'll also be starting to slowly build up my military, trying to get a defender or two (upgraded to whatever weapon level I have) onto each planet. I'll generally have the econ sliders set to make only a few credits profit, with a the production being divvied up between some military, more social and lots of research.
Don't set your sliders and leave them, instead adjust for whatever your current needs are, because you don't want to do anything slowly. If you need more infrastructure, then go 100% social spending. If you have good military techs, then go 100% military spending to take advantage of those techs ASAP.
Also, should have your total spending at 100% almost all the time. If you have to drop that lower than 100%, that means you've built too many factories/labs, and not enough markets. Making a profit at 100% spending should be one of your first goals after the colonization phase, and you should try to achieve it quickly.
Popcorn Avenger is right about Diplomacy and military might. It's much easier to survive by staying at peace than to try and fight off attackers in a war.