For a starter system look at Blink. They use AA lithium batteries and can be installed anywhere without running power. Batteries last for several years depending on usage. Storage is free up to a certain number of clips (IMO no need to keep clips unless it is nefarious). Can run 5V power to the cameras if you want. Look for a Black Friday sale for the three camera system for around $150-$170.
It's not perfect but for a minimal investment you'll be up and running with simple motion detection cameras and through experimentation will give you an idea of what you want in a more robust system.