I have a Seiko self-winding non-diver's watch which I love. It was $88 shipped, which is a deal for what you get. However, it's rated as splash proof only. Many people report they are fine for showering/swimming, though.
The diver models have much better seals and there's no reason that you can't, uh, dive with them.
The affordable Seiko self-winding mechanism runs about 20 sec/day fast when new, but supposedly can be less than 10 sec/day fast when broken in.
Personally I really like a mechanical watch, because little gears are NEAT. But they are not as accurate as quartz movements.
There are other ways to get self-powered watches... these are the ones that come to mind.
Citizen Eco-Drive: light charges a capacitor
Casio Solar: Same. You can get a self-powered G-shock that syncs to atomic time for about $100. Neat! It should also handle dive depths, though it doesn't have diver features.
Seiko Kinetic: Mechanical device charges a capacitor.
Some of the self-charging ones have really neat features, like a power reserve indicator, perpetual calendar, or sleep mode. (The watch stops moving the hands when power is low, and resyncs them when you wear it again. You could put it in a drawer for years and use it right away.)
I had good luck with this site:
21Jewels - Wide Selection of Sports and Fashion Watches