My goal was to find something small, light-weight, and in the same price range as a GoPro.
I found two promising options:
I went with the Sony, although it cost me $100 more than the Panasonic, and also more than GoPro HD Hero2. People really seem to like the video quality. The image stabilization supposedly doesn't introduce any jerkiness (watch out for this!), and the videos I found from the DSC-HX9 (a similar, lower-end model from last year) looked pretty good. And reviewers who have compared them say the 2012 HX-series models have even better video. It also sounds like possibly a better still camera than the Panasonic, but it's too new to have any professional reviews.
Of course, you can always go higher-end (although they'll suffer from significant additional weight) and I'm sure some of the dedicated camcorders would work well. My rationale for a point-and-shoot is that if it doesn't work out well or if I upgrade to the HD Hero3 (next year or whenever it comes out), I figured a decent, compact point-and-shoot might still be useful to me or another family member.
Well, I'll definitely let you guys know what I think. I plan to post up some vids in this thread, within a few weeks. Maybe not at full res, but probably 60 fps so you can check out the image stabilization.
As for trying to control vibration, I found this:
Rubber Vibration Dampening Mount, #1/4-20 x .25"L Double Threaded Mount, .43"OD x .4"L Rubber
It might not do anything for me, but at least the price is right!
Oh, and never try to buy the cheapest memory card you can find. At best, your recordings will be choppy. At worst, they might just cut out completely. Always try to get a card that has some good reviews and is at least in the middle of the pack, performance-wise, for the class you need.