You'll see a lot of people using Games Workshop, P3 (from Privateer Press), Vallejo, and Reaper paints. They're all good options though here are a couple of things to consider...
1) GW and P3 come in pots while Vallejo and Reaper come in dropper bottles. If you just want to dip your brush in the paint and go, pots are great. If you want to mix colors (for which you'd need some sort of palette), I think dropper bottles are much easier to work with.
2) You can buy paints online, but being able to stop by your local hobby shop and pick up a couple colors is very convenient. I really like Reaper but no one near me carries them. That's okay when I want to order a bunch of paints (shipping is free on large orders), but if I just want to get one paint the shipping cost really isn't worth it.
3) If you are planning to mix colors, consider making a wet palette. Just google wet palette and you'll find some how to's. It's cheap, easy, and you probably have everything you'll need already. Here's one tutorial, there are plenty of others:
http://massivevoodoo.blogspot.com/2009/10/tutorial-wet-palette.html
Lastly I'll make my plug for Reaper Master Series paints. They're what I use (though I do have colors from other brands). They're conveniently organized into groups of shadow, mid tone, and highlight which can make things much easier for beginners. That being said, you will be fine with any of the major brands.
Here are a few other 'just starting' threads that might be helpful to look over:
http://www.coolminiornot.com/forums...ooking-to-start-painting-have-a-few-questions
http://www.coolminiornot.com/forums/...upply-question
http://www.coolminiornot.com/forums/...int-high-elves
http://www.coolminiornot.com/forums/...rst-Submission