GoPro is the camera of choice for amatuer action video...
It comes with sticky mounts for your helmet and is well protected from the elements in a clear plastic shell...
... on the bad side,... it's very tiny, and has a single button cycling menu that is hard to operate or see...
Here's a link...
http://www.goprocamera.com/For smooth video on a bike,... helmet mount is the best, and a camera with a wide angle lens will show less jiggle...
My point and shoot camera is 25.5mm wide angle,.. the GoPro camera is even wider,...probably about 20 or 22mm...
For editing,... I just use the Windows Moviemaker that is built in to Windows Xp... It's not the greatest, but it's good enough, and it's already on my computer...