Is the NVR/home computer dedicated to the camera security system?
If so, I would put all three cameras and the "NVR" on the POE switch provided that it is truly a switch and can keep the traffic amongst the cameras and NVR/home computer (with "included software") from the main network. I.e., a smart POE switch that you can manage.
Otherwise the NVR/home computer could go directly to the router and the router directs the traffic. Plus you may, depending on the router, establish priorities, for the port being used for recording on the NVR/home computer.
Does that all fit in with your concept?