This topic has been done to death here many times
My little input this time is that IMHO one will soon get fed up with the distorted image produced by most cheap cameras. So try to get something that produces a proper rectangular frame. I used the Dogcam and it was basically crap. There is a video in
this trip writeup.
The shutter/prop effects are also naff. All the little cameras suffer from them - LCD or CMOS are mostly marketing names for similar technology. It is caused by a very fast shutter speed; the cheap cams don't have an iris so use shutter speed as the only means of controlling the aperture. Consequently, sometimes, putting a neutral density filter on the front can alleviate the issue, by reducing the light coming in and forcing the camera to use a slower shutter speed. But a manual-shutter speed camera is the only decent solution.
Now I use a Canon Legria G10 which has a manual shutter and at 1/120 or slower (which is ~ 1/10 to 1/50 of the shutter speed of the cheapo cams) one can shoot straight through the prop and one just sees a slightly visible arc which is as it should be. But it wasn't exactly cheap. I also have a proper anti-vib mount for it with massive suction pads for mounting it on the windscreen.