The advantage of a helmet mount is that the camera looks where you look. That can be a disadvantage, too, depending on what you're trying to capture.


The advantage of a chest mount is that the camera captures what you "see" in front of the bike, and not what your head is turning to see. It gives a lower angle, as well, which can be cool.


Mounting on the stem, or handlebar, is going to produce some vibration that may, or may not, be welcome in your videos. I doubt there is any way to secure the camera to your bike that will prevent it being stolen. That's another advantage of the chest and helmet mounts.


All of the myriad "action cams" that are currently available are probably good enough for most people. One of the advantages of the GoPro models is that they are ubiquitous, such that there are ample accessories available, and lots of online tech support. I don't know if the least expensive model will meet your needs. You'll need to do some research. Consider things like weight, batteries, mounts, cases, and other accessories when making a decision. Don't forget that you'll need storage media for your pictures and videos. Might as well get some SD cards (or whatever the camera you choose requires), when you make the purchase.