Having done a lot of research before installing a back-up camera. Emm-dee is correct, there is a lot of junk out there. Spend your money on a decent camera and you won't be disappointed.
I opted to do a hard-wire install and chose a Boyo license plate camera: Amazon.com: Boyo VTL375 Ultra Slim Zinc Metal Black License Plate Camera: Car Electronics
This camera can be integrated with an in-dash head unit, a separate monitor, or some GPS units. You would have to do some research, because the wiring type may differ with the monitoring choice. I was first going to use an on-dash GPS that had a port (which many do). "Our choice" (aka DW) was to do an in-dash head unit with GPS.
The Boyo is a quality camera- function and finish are excellent. This camera is nearly invisible as it appears to be nothing more than a license plate frame. Mounted on a 2013 Siverado, I have adjusted the camera to just catch the hitch ball. The nearly un-distorted wide angle camera catches an approx 170 degrees clear view for a least a city block. I chose a permanent install because it makes a world of difference in everyday driving. It is particularly useful when backing out of a parking stall and your vision is obstructed by vehicle next to you. Note that the Boyo camera also has excellent night vision capability even though it doesn't have infra red. I can line up the hitch at night with only the back-up light illumination and no help. Ours has had flawless operation for 3 years. Like any camera, the picture may blur with rain.
Two other tips:
1. I had to wire to the back-up lights and DW insisted that I install after-market back-up sensors. As always, DW is always right. It is an excellent combination and the sensors are accurate to the inch.
2. Even with a back-up camera, day or night, lining the ball up to the hitch is challenging when it's black on black. So I took a spray can of international orange and painted the front couple inches of the trailor hitch cup. What a difference when you are trying to line up on a 4" target!