Hi Malcolm,
Serious action camera users seem to go for GoPro. Geat quality and loads of accessories but all at a price.
I do a fair amount of country sports and some time ago bought a camera called Zennox. It is presently on offer at Norris of Penrith for about £16 (a considerable saving on what I paid!) and comes with a variety of mounts, also a waterproof case.
As to where to put, no roll bar is a bit of a shame, and I think you would need to experiment. Rather easy would be the badge bar and cross head lower arm. Also crash helmet though I have doubts this would be allowed.
You may need to be a little creative and it's a shame it's not wifi but for £16 !!!
Hope this helps.
Geof