Check out the Xiaomi Yi. Here's a test video showing it compared to a GoPro. The Xiaomi Yi 2 shoots 4k and is $200 on Amazon. It has its own version of a mounted case, but it will work with GoPro accessories. Amazon sells these Chinese knockoff accessories for super cheap. I got this for $10 a few months ago and they're all pretty good quality. I mean it's just plastic, and the mount stickies are still the same 3M brand GoPro uses. Selfie stick is kinda crumby though.

Might also look at getting a GoPro on Ebay or Craigslist. I picked up a new Session for like $100.