I've built camera systems for applications like para gliding, investigative journalism etc. we've made a systems work for filming on the bikes both mountain bikes and motorbikes. the key is power, duration of filming and what you want from the footage these are things to consider and these are my views so take'em with a pinch of salt.
main points
DVD quality and what you should aim for is 720x576 resolution there are lots of cameras which promise it but can't deliver some of the small SD range get close 640x480 but that's the full area. We're now in the realms of underscan and overscan another debate.... for another day.
What do you want from the camera? holiday shots, just bits on the bike? what do you hope to achieve?
It might be best to have 2 cameras one for bike one for general footage....
formats.... HD SD 4x3 16x9 or 5x4....
So here we go
1. small cameras need more light to work well and give results
2. helmet mounted cameras as the name suggests are on your head and your head moves around loads even with the natural dampening... so you may not get the results you want. Or you may put yourself in hospital trying to get a shot....

done that...thanks.
3. mounted systems are nice but again watching hours of vignetted (cropped) footage of the front wheel going round is slightly more boring than watching paint dry.
4. whatever system you get you need to consider what you want to do with it.
5. Once you've worked out how your going to deal with the material you've captured to turn it into a record of your trip. It will become apparent which camera is the best for the application.
6. Tape Versus Tape-less good argument tape is a physical thing which you can look at and touch tapeless is more frightening. I've deleted a number of really good stuff by accident....

7. HD (high def) versus SD (standard def) I love HD whats best you can do more with it in post production when you auther down to SD...

8. cheap versus expensive the more you spend the better the footage, cheap is less painful when you drop the thing into water.
All small cameras can ever be is part of the overall solution look at any... production....
what you see is
never what actually happened in order of events, locations and words spoken.
I love the idea of shooting good stills and video on one camera you might want to consider that as well.
So to be honest there's no direct answer to your question an on bike systems whatever it is will not make the story for you. that bit the creative idea is yours and yours alone.
hope that helps I'm now going to cause hassle else where....
