Just another thought. We have a hunting camp in the Michigan UP. We have had it broken into a couple of times, it's a former logging camp built in the 1930's, it's huge (sleeps over 20 people) and was full of antiques. So we started thinking about adding security, like you we have no phone lines, but we do have power. We decided against it, as it's so remote that police response time would be over an hour, and then they would have to find it, it's not visible from the road. Thieves would be long gone by the time anyone got there.
Your place may not be that remote.