If you mean individual batteries for each camera, I think you won't be happy in the long term because of short battery life. I would use POE (power over Ethernet) cameras with the router powered by 12v from the house batteries. Solar to maintain if you're not plugged in.
There are systems that will work without fixed IP, I have one. Uses DNS.
Some cellular hotspots will not support the port forwarding features typically used to remotely access the system. Wireless companies are not enthusiastic about supporting servers.
Most people would do better hiring this done by a security company because it is not just plug and play. If you want reliability.