There is a huge spectrum of options with your classic price/performance/quality tradeoffs.

I started out with a Hobbyking wing camera, that was basically a cheap action camera module with a single cell LiPo and micro SD card slot wrapped in clear heatshrink tubing. For the $35'ish that I spent, it worked pretty well, but is no longer available from them. Stuck it on the roof of my TC for a dead rubber A3 once: After about 6 years it failed, so I went looking for options. I have a GoPro Hero Session 4, but it was on the heavy side for some of my use cases. I ended up buying a RunCam 2 (https://shop.runcam.com/runcam2/) which is not too bad and has built-in WiFi for preview and configuration. I often stick it on my hat to record races:
There are plenty of other candidates around, but I don't have direct experience. If you're prepared to go cheap and gamble on shipping times, Aliexpress has action cameras for close to $10.

You could also look at the pretty big field of FPV cameras which also start pretty cheaply.