I have a wifi webcam with no Internet access at my front door. It doesn't need Internet access (in fact, it's blocked from going outside the router). It's happily streaming video onto my home network. I just open the stream in VLC on any device to see the live video feed instantly. Easy to make a shortcut that opens the address in VLC.

Video is also being archived locally elsewhere on my home network, but no outside hosting is needed for either instant live access or home archiving. Just a minimum of research.

When shopping for a camera, only buy one that has ONVIF compatability. Then you can use it with third party apps.