Here is the link for the camera I bought a few years ago. It has been updated a bit but it's the same camera. It's res is 640X480, which is good for web use. I like the camera, it is small, light and does what I needed it to do. As far as stabilization, I had no issue with it and the price was right. It's around 124 on their website. When I got the two I have they were under a hundred bucks.
http://www2.oregonscientific.com/shop/product.asp?cid=8&scid=107&pid=824
That camera was just on sale at Sam's Club for $48. I took mine back because of quality on a big screen.
I've used a MiniDV with a home-made gun handle for left handed use. Keep it in a magnetic tank bag, and can get it up and running in just a few seconds, with left hand. Handy to shoot other riders, road in front, road in back, view to the side, or your own face

. Even with stabilization, your arm 'suspension' helps, too.
You do need to be able to ride one-handed. Upshifts without clutch no problem; downshifts, you plop the camera into the open bag pretty quick (plan ahead). Got some fun footage on the Dragon with this setup, keeping my speed around 35 (weekday, no crowd). Works pretty good... in rain, not so much. Cigar smoke clouding the picture? Nah...never been an issue.
Had a lightweight (cheap) handlebar mount for a while, but pic was too shaky. Then it went and broke just as we were heading down the old gravel railbed off the Blue Ridge couple years ago; almost kissed that camera bye-bye. Couldn't hand-hold on that trail though, so a helmet mount would have been good.
Yeah, yeah, I know it's not the smartest thing to do, but that's me. And, when filming from farther back in a group, some viewers have seen some dumb things
they've done, like riding the center line. Or holding a camera while riding.

:-Jerry