We have a home in the States, only occupied by ourselves when visiting. I set up 5 interior Nest cameras (situated so all doors/windows are monitored) and one exterior over a back entrance. I also set up a Hue lighting system which you can program to have different schedules for different rooms/days. Cameras are infrared. You set notifications according to what you do or don't want to know about (sound, motion, person, etc). You can also talk to someone through the camera system.

I probably spent under $1000 in all.

Yes, all components are dependent on internet and power source, but tbh, you're just trying to either slow them down or encourage them to go elsewhere. If they are dedicated enough to kill the power before entering, they're coming in cameras or no cameras.

Good luck!

First I would ask myself what good does a surveillance system serve.

IMHO: nothing other than having a video of your house being broken into.

You need some deterrent: timed lights, fake cameras, beware of dog signs, at most a siren to scare away thiefs if they break a window.