I would always go for a camera that is a good stand-alone camera that the manufacturer makes an u/w housing for. Don't have to use that housing - though I usually do - as Ikelite make housings for quite a few popular cameras out there. I would avoid cameras made/marketed especially for diving, as the camera is always of lower quality.
For me, I would always choose a camera that can shoot in RAW as every u/w picture needs some post-processing, and it's far easier and more effective if you start with a RAW image.
The one brand I've consistently had most success with, not just in initial design/performance but also in after-sales service, is Canon. Though funnily enough I get underwater results from my 15mp Canon G10 in Canon's underwater housing that are no better than from my 5mp Casio EX-Z55 in their housing. But if the Casio ever breaks it's irrepairable and is junk. That's true of most brands of compact camera. Canon stand by and will repair any camera they make.
You want to go for a camera that takes a proprietary battery. Pretty well all these days have excellent battery life that will last many dives, so you never need to open the housing out on a boat or on a beach somewhere. All the "purpose-made" underwater cameras I have seen, such as the Sea-and-Sea or Sealife ones, use AA batteries that will NOT last a full day's diving.
Remember, when you take a camera underwater it's not a question of whether it will flood, but when. Bear that in mind when you decide how much to spend, but do try to be meticulous and conscientious EVERY time you prep your camera/housing to go underwater.