Have you looked at the Sticky? There are many choices with discussions and images linked in there.
There is no "best" choice - each person has different criteria, including budget, interest, likes/dislikes etc - so there is no one right answer.
A camera series I think meets virtually all of the essential criteria I personally have for those wanting to get into uw photo are the Canon A series. I just purchased two more Canon A570IS cameras with Canon housings for our hire cameras and I find myself using one of them all the time on land and usually taking one with me on my dives, too LOL They're just fun and easy, but have enough room to grow as you learn and discover what you like. newegg has a deal on them for camera $140 with free shippping; housings are about $160ish.
These are not the only cameras that allow this, but they produce some of the most consistently good results from most users that I have seen. Have a look at recents threads in the UW area, including the sub forums, too. There are quite a few people on the same quest as you are and it's often helpful to read around a bit.
A quick list of what to look for at a minimum:
- manual controls of both aperture and shutter
- manual ISO control
- manual white balance
- housing available
All compacts have various auto settings if you don't want to start in manual modes - but you'll likely regret getting a camera that doesn't give you the manual option and simply end up buying a new camera before you'd need to if you went with one with manual controls in the first place.