I get a fair number of inquiries about which camera to get for starting out with underwater photography, so I'll chime in with a few of my thoughts here.
Many people think you have to get a dedicated underwater camera, while this may be the best for some people, it isn't the only way to go. Oftentimes you can pick up a great new camera, with all the bells and whistles, and it'll have a corresponding manufacturer designed underwater housing that is good to about 130-140 feet or so. In many cases you can even find a housing available for a digital camera you may already own. There are housings avaiable for many Sony, Nikon, Olympus, Casio, Canon and Fuji cameras already on the market, and they seem to be committed to supporting housings in the future. there's probablay a couple others I have forgotten. Below are some examples available at Amazon.com. You can refresh the page for more examples, or I suspect do a search for specific cameras and housings when you get to a results page. Note: Some of the lower priced housings here are geared to snorkeling depths, make sure to read the fine print.
Remember, each housing is generally made for a specific model of camera. If you have camera and are looking for the housing, you can always reverse the process and look up the camera and see if the housing is available as an accessory. Older models may be problematic as they get discontinued as cameras are phased out.
Having picked up our first digital camera and housing in about 2000/2001, Pat and I have been upgrading as time goes so I'm semi-familiar with what's out there. I'm not going to recommend specific cameras(The big photo show is at the end of the month - everyone will probably introduce new cameras and today's stuff will be out of date shortly anyway), but Canon, Olympus and Fuji seem to be the most popular with the semi-serious underwater hobyists. I wouldn't hesitate to house a Nikon, Casio, or Sony either though. Many of the more popular point and shoots even have underwater settings built in these days.
Some basic recommendations I'd give are...
LCD screen, get it as big as possible. You'll probably want at least a 2.5 inch screeen, LCD screens that size and up are much more forgiving to middle-aged eyes, plus you'll see more detail in what you're doing while taking the photo.
Optical zoom is more important than digital zoom, you are probabaly looking at 3X-6X or so optical zoom for underwater, although I've heard people are happy with their superzoom cameras underwater, they just don't use the full zoom capacity underwater.
If you are going to be serious about it, and have access to nicer image editing programs, you might consider getting a camera with RAW. At the very least I'd recommend getting a camera with a "Manual" or "Custom" white balance setting.
Many people think they have to invest in external strobes and the whole shebang right up front. That's really not the case. Take a look through my archives, there's not a picture on the blog yet that used an external strobe. They were all done with the onboard flash or with natural light. People who know what to look for can tell if an external strobe was used or not in some shots, but most people who aren't really into the hobby can't or won't care. External strobes will allow you to do more things, and get you well lit shots from further away, but you can always add them later if you don't right away.
Many of the underwater housings suitable for diving depths are running in the $150 to $225 range and corresponding cameras can run anywhere from $150 and up, but you can often get into a pretty decent little setup from $300 to $650 these days. There are higher end cameras and housings available of course.... it seems once you get hooked there's always the desire to upgrade.
Anyway, once you've got your equipment together, the best thing you can do is get to know your camera, and practice.... It's almost a lock you'll be disappointed with your initial results at first, I was, but with practice you'll get to know what you can and can't do with what you have.