>>2294493with such a low budget you'll want to look for second hand. You can get pretty decent stuff that just aint the norm anymore like 720p or 1080p cameras. Back in uh... 2012 i think I bought a Midland XTC400 for about $200 new. Quality isn't the best especially today and support for it is long gone but hey, it works and i can strap it on helmet/car/rifle/tank turret/tree, with its (manually) rotating sensor it's very versatile and was the reason I went for it instead of gopro, also that the case is long rather than wide. It suffers from low light tho but hey, you're on a budget so better not be picky.
Picrel is a snapshot purposely of mid quality from a video of my trip to norway. A few droplets blur some spots and I'm driving between 80 and 120km/h there, 7am in an overcast october. It's not glorious but it works, and it looks better when you get everything moving as in a video