We used to have ADT, we recently switched to a local company (Guardian) for upgraded features.
We didn't have any issue with ADT while we had them, but as soon as we cancelled their service realized that if there HAD ever been a break-in... ADT was next to useless.
We called ADT to cancel, and then had their system disconnected and the new system installed.
TWO WEEKS LATER, ADT called us to say, "We've detected that your phone lines have been disconnected or cut. Do you want us to investigate a potential break-in?"
US: "Um, we cancelled and disconnected your service two weeks ago..."
ADT: "Oh, well, we only check the disconnection alerts once a month or so, so we just didn't see it until now."
US: :yikes:
Basically, if a burglar HAD cut our phone line to deactivate our alarm system, they could have robbed us blind and/or murdered us, and ADT wouldn't have noticed anything amiss for WEEKS, much less sound an alarm or call the police.
Our new system is wireless, so there are no phone lines to cut. I'm glad we made the switch.
ETA: Long story short, I would do your research on local alarm companies. Find out what options they have for your specific situation. Since you mentioned no phone/internet... wireless may be the way to go, or you can also consider just putting in a no-frills landline, if the price to upgrade to a wireless system is too high (it's a pretty pricey upgrade... *sigh*)
Also... sorry about my rant. It probably wasn't all that useful.