If you prefer to use a vented helmet, one option for attaching your action camera is the GoPro Vented Helmet Strap Mount. It's made by GoPro and has the same quality you would expect from its camera.

It’s tricky to capture a first-person view. You could munch on GoPro’s Bite Mouth Mount. Or for a solution that makes you look marginally less eccentric, you could strap this band to your bonce.