If you don't want to spring for a GoPro, SJCAM are pretty commonly used for FPV recording. SJ4000 is a common economy action cam that often is rebranded and put into different housings. I'm pretty sure mine is fake though, so be careful!
If you decide to get goggles and fly FPV later on, none of these action cameras will make a good flight camera, they are too laggy. You will need to add one of those tiny, low resolution ones to fly with.