A practical beginner route is usually either:

1. A compact camera with a proper underwater housing, or
2. Your DSLR in a quality housing if you’re ready for the cost and bulk.

The community consensus is that underwater photography is rewarding but not cheap. A compact setup is often the easiest and least risky place to start, and housings are available for some Canon and Olympus compacts that are suitable for real diving depths (around 30 m was mentioned), not just shallow snorkeling. Good results are possible from compact cameras, especially with an external strobe.

A DSLR in a housing can produce better results, but it becomes much more expensive and complex. If you go that route, buy quality housing gear and add pieces gradually so you can learn the setup.

For lighting, an external underwater strobe is strongly recommended as you progress. For lenses, the shared experience here mentions using a 50mm on a DSLR, but in general the best lens depends on your subjects and housing/port options. The key point is that lens choice is tied to the housing system.

So: start with a compact plus proper dive-rated housing if budget matters; move to a DSLR housing later if you want the best image quality.