Simplicam

Camera uses wifi for all communications.  The SS base station will report an event and sent that data to SS.  SS will then send a command to the camera to start recording.  If you are concerned about the bad guy cutting power prior to breaking in plug the camera into a ups to give it a battery backup.  You will also want your internet gear on a UPS as well because if the power gets cut and you lose internet, you lose camera.

You can also ask (should ask) your internet provider to security-harden your demarcation point.  That's where the service comes into your house.  Most any thief who's not a completely-gone, smash-and-grab meth-head knows to cut any and all visible wires going into a house.  if they are savvy enough to cut the AC without getting killed, for-sure they will know to cut "comms".

Hardening the "demarc" involves moving any junction boxes into your house and either hiding the entry point by bringing the wiring/fiber into the house underground, or enclosing the wires/fiber and entry point in steel pipes bolted to the house.  If you have overhead lines it involves raising the entry point out of easy reach (and still securing any junction boxes).  Most providers will charge money for securing the demarc, some do not.

This is a very informative interview with a repentant former thief:
https://www.youtube.com/watch?v=DtwD-c9hn58