You have an abundance of options even for inexpensive rigs. I won't recommend a specific setup because I'm not up on the latest, but both Canon and Olympus make small, inexpensive housings for most of their cameras, and have for some time. There are other housing makers as well, but other than Ikelite - who make excellent but heavier/bulkier/pricier offerings - I don't follow them. For shallow tropical pics you don't need an external strobe, but might like to have a red filter (like URPro and others) to help balance colors below 15 ft. My advice also would be to pick one of the point and shoot cameras that has a relatively wide angle and fast lens (small F-stop number at the widest zoom setting). Also get one that permits manual control of aperture and shutter speed, as well as the typical auto exposure mode. You don't need anything above the standard 3X optical zoom, telephoto is useless under water. Get one with a big LCD monitor. A lot of folks like RAW shooting format capability, for the power it affords in fixing up the pictures on your computer afterwards, but there are few inexpensive cameras that take RAW format. It's certainly not necessary to get good pics. Also, I think it used to be more economical to stick with cameras that could use alkaline or NiMH AA batteries, but the proprietary batteries seem to be very good now, and not expensive esp. if you don't buy the camera-branded make (you can often get higher capacity in the aftermarket batteries too). In my case I most like my 7MP Canon S-70, which takes RAW format, has an inexpensive proprietary battery, inexpensive case, and the controls and menus are laid out well for my simple use. I can get two dives @ 100+ pics each dive on a single battery. I bought everything used, except some of the batteries, and have no regrets. Not recommending this one as optimal (shutter lag is probably slower than most these days and the LCD is small), but as an example, you could buy the camera and case for $250 or less on eBay. There are numerous other excellent condition used rigs in that price range.
