You are going to get the best quality video with a Mini-DV camcorder. You can get a used Canon Mini-DV camcorder on Ebay for about $100-$120 but you need to make sure it has a analog av input in which you can plug in a bullet camera with microphone. Canons aren't the only ones with these inputs but most canons do. You can get a SONY bullet cam with microphone and helmet strap for $120. Strap the cam to your lid, hit record, and throw the camcorder into your pack and you're ready to go.
Here is a link that is a guide as to which camcorders have an av input.
Helmet cameras Compatible camcorders with an a/v input