Personally, I haven't had much luck with the cheap little cameras. I've bought six or seven of them. The one I got from BayouRat Rocketry is the only one that really works.
If you're willing to go up to $100, you can get a nicer camera than the key fob or "gum stick" ones.
The Boostervision GearCam DVR-II, for example, is just a little more than $100. It works well and is almost as small as the cheaper cameras. It takes better video and doesn't put a timestamp on the video. If you search for "helmet camera" or whatever, you'll find that there are a variety of cameras made for recording action videos that will work well on rockets. Check the reviews though, to avoid problems with the cheap imports.
What I do is to check out the close-out aisles at stores like BestBuy or WalMart for returned, open box, or discountinued cameras. I've bought a few cameras for under $100 just for use in rockets.
I like the AIPTek-style memory card cameras. They are too big for model rockets, but fit in mid-power and high-power rockets. They take much better video than the little pinhole cameras, have controls that are easier to operate, and have an LCD screen for reviewing the settings and video. The newer ones have rechargeable batteries and record for at least 40 minutes on a charge.
The box-shape with the lens on one corner makes them easy to mount in a rocket. I just make a box in the body tube that the camera slips into. (See:
https://www.rocketryforum.com/showthread.php?t=10846&page=2). This allows me to turn on the camera and put it in the rocket when the rocket is on the launch pad, ready to go.
-- Roger