Stick to the GoPro style action cameras. When riding a bike they cannot be beat. The only choice you have after that is which brand you trust the most to give you the quality footage and features you want.

GoPro is the signature action camera so you can't go wrong there. They are also voice activated. However, they're also the most expensive and may be more camera than you want or have any need for.

The best thing about these style of camera is they give you the most versatile and stable mounting hardware available. I can literally mount mine securely from head to toe.