We have a security system, but not with brinks or adt. Our system was already installed when we purchased the joint. The yearly fee is cheap $10 per month (when paid yearly) if hooked up through a landline, $20 a month if through a cell. There is a battery back-up
supposedly good for six hours. I say
supposedly because it died a bit before that durning a day long power outage.
The most expensive part is installation or, if you got free installation, fixing something later. Wiring does get old and need to be replaced (they charge a LOT to replace this stuff).
All the doors are wired, and so are the windows. Anytime something is opened you hear a buzz. The control panel also shows you what door or window is currently open (as long as you know what area on the control panel corresponds to what door or window). See if there are newer panels that are more explanatory. It will be worth your sanity.

We also have indoor motion detectors - if you have a pet find out how to set those correctly when you are away from the house.
Since our municipality charges after the third false alarm, the alarm company calls us before they send the police or fire department. We need to pick up and respond with the code word. NYS requires hard-wired smoke detectors with any permit-issued work now, so we are also wired for smoke detectors. When the smoke alarm went off, they called before they sent the fire department (I just told her my husband was cooking dinner.

) If there is no answer, or if the person answering the phone does not know the code word, they send police or fire. They even called when the battery back-up died.
We also have remote alarms for the upstairs as the panels are located near entrances.