Weird questions mate...
I do a lot of clipping for freestyle, tried 3 times on-board cameras, but too much spinning, one sees nothing useful.
But just to answer...
Gender: every woman I've been has always come back for seconds...

Age: old, but not acting my age.
Water depth: weird mate. You have to worry about nasty falls and shock a lot more than depth.
Material: not relevant. Make it sturdy.
Where: that question doesn't work, it depends what you're making the movie for. For Tube clips showing freestyle, I find none works. For straight sailing, most of them work, but then it gets boring to watch. Nothing like an outside view, which is basically 99% of all Tubes.
Finish, buttons: you're kidding, right? This sounds like a kitchen Tupperware question...
Battery life: longer the better. More than 1-2 hours.
Screen: you're kidding, right? I find looking back at movies on the peddly little screens don't work for outside cameras, let alone on-board ones.
Shots: gotta be video. Stills and 1-sec action shots are not useful with head cams or mast cams. It's hard enough to make useful videos with on-board cams...
$$: none here. I find they don't work again, personal opinion.
Hope I didn't rain on your parade, hope some of this was useful to your project.