I would read and thoroughly digest the reviews Mat posts on his
Techmoan website. His current top picks for action cameras:
The GitUp Git2 is the best budget camera with a mic in, the Dazzne P2 is the cheapest camera with good performance and the Yi 4K is the best 4K action camera I've tested (and probably the best one full stop).
Personally, I use a Sony AS30v, which I found second-hand in a branch of London Camera Exchange. I like it for its stabilisation, its handling of exposure, and ease of use, but the hardware is rather overdesigned.