I suggest a GoPro 3 silver (the 3+ has a cheaper, thinner case!) you wont need the remote the black has (we havnt even used ours)
On top of the helmet i believe would be the best spot. Sides it looks funny, and really bad when half the video is your helmet!
Many different places can be used on the blaster. I suggest a bar mount, which you can put on many places. Bars, front bumper, upper a-arm, nerf bars etc. Another nice thing about the bar mount, you can get a 3/4" pvc pipe inside of a 1" pvc, plus a 1" end cap (little tape inside holds it tight) and you have a $5 gopro extendable stick than would have cost you $50+ normally. A stick is useful for many angles and different shots (not on quads much). Snowboarding/skiing you can turn it towards you and do tricks, away from you and more steadily video others. You can use it as a short boom and get higher speed pics and vids (focus on the moving object, blur around it).
A professional camera thing i saw once was a 40' carbon fiber rod, on a moving pivot point. He could get still action pictures of cars doing 120+ mph (car still, surroundings blurred). Really cool pictures, but i doubt you have a few grand to blow on a stick I:I