I have a GoPro, but it's an older, lesser-expensive model. It will stream directly to a monitor, but it only has about a 45-minute battery life in video mode. Video is excellent - HD quality (or not, depending on settings). It can be wired to a power source, but input is 5v (USB). Also, not sure whether or not you can set them to come on automatically when power is detected. Mine has to be turned on manually, which would be a pain as a backup camera. The newer ones have remotes which could be used to turn it on and off, but I prefer a backup camera to go on and off with the ignition. Others prefer to wire it into the truck's backup lights so it only comes on when in reverse.
If you can wire another camera to your existing rear-view monitor, that would be the least expensive way to go. I have
one of these which works great, but doesn't have the infra red night vision (I have rear flood lights so don't need it). Has RCA jacks to connect power and a monitor.