I do sometimes use a very cheap (~£10) "Muvi" copy on my Lid, the footage is generally pretty toss, but can still be a nice reminer of your descents when it does come out OK, I've also go one of the old Oregon "Action Cams knocking about somewhere, very robust housing, runs of AAs but I never shot anything worth watching on it, Hmmm might un-Earth it actually see if use can be made of it again...
your 2nd worry is the main one really. if you can get a helmet cam mounted at the right angle then you might get good footage, it often depends on how rough the trail and your riding is that particular day...
Mounting on you chest/shoulder can work better as it seems to be more stable, however I always seem to angle it too far down and get lots of ground in the frame, it would seem my torso is angled more towards the ground than I manage to estimate when positioning the camera, have a few practises before your trip just to be sure you are not shooting lots of ground or sky...
Mounting on the Bike is a Non starter in my book, too much vibration and the only people who ever seem to do this go and point the camera at the suspension components of their bike so they can have a "kinematics" **** off later "OOOh look at the bump response over those roots", you want to shoot the trail not the bike...
TBH unless you are a riding God, riding with other riding Gods I can't see the point in buying a Go-pro or other similarly expensive units just to post boring films of joe-average "free-trundling" on youtube, but I'm all in favour of us mortals being able to capture our own riding for a bit of a review later, just get a cheap binable micro SD cam...