There are a lot of possibilities to do what you are asking.
If you use a standard residential alarm system and want to operate it off of a solar panel the following will be needed. Deep cycle battery with charger and solar panel about 16" x 18" in size. This will depend on the amount of available sunshine year round. Basically you need to replace used amps so that the battery does not run dry. Must consider the amount of amps or watts needed based upon all components that are attached to the battery for power. Remember it is will be running 24/7.
Next you will need a panel that can be tricked to not be in trouble with out any AC power. Some panels can do this if you connect 12vdc to one of the 16.5ac power input terminals. The panel that I used in a similar project sadly is no longer manufactured. The project was a cabin on top of a mountain that had no utility power, only generator when owner was on site 4 -5 times a year. Works great!!! Was even monitored with cellular but no police dispatch since there were 3 locked gates to get thru.
Some of the other suggestions will work quite well. Considering the cost of putting together your own system (including your time for the learning curve and troubleshooting) they can be the better price.
Hope this helps.
Les