In my current house I have a professional alarm, not with ADT but with a major local security company. They have their own monitoring station and my alarm phones them if it goes off. They can see from the signal if it is just one sensor, or if several sensors have gone off (e.g. back door opened, person in hall, person in front room or going upstairs). More than one sensor means a Confirmed Alarm and the police will accept it. Just one sensor suggests a false alarm and police will not respond unless e.g. a neighbour reports seeing suspicious character climbing in. The monitoring station also calls down the list of keyholders until someone agrees to go and open up. I actually also pay a local security guard co to be keyholders and attend if no-one else answers. It is hard wired to a phone line. It cost, from memory, a few thousand and I pay an annual fee of a few hundred. I also pay a couple of hundred a year to the guards, and an hourly fee (might be £30 or £50) if they are called out and attend.
The alarm beeps inside the house when the garage door or back door is opened, even when the alarm is not set, in case somebody attempts to creep in unnoticed.
I have a similar arrangement at my commercial premises.
I have also used DIY wireless alarms by Yale, at a fraction of the cost, and fitted myself in half a day. They do one at £180. I think the phone callout to keyholders is essential. You need to hide the alarm panel and its phone connection where an intruder will not find it before it has had time to start the siren and dial out. You can have a remote keypad near the front door.
Depending on your circumstances, either option might be suitable for your pocket and your risk profile. If you keep, e.g. family gold for weddings or festivals, this will become known and may attract serious intruders. If your only concern is teenage crack-heads smashing a window or kicking in a door, they will probably not try to defeat even a simple alarm.
Start by fitting proper locks on your doors and windows, and use them, and don't leave the keys on the locks. I am particularly unkeen on plastic doors with Eurocylinder locks. If you look on YouTube you will see why.