chrisf,
A quick, inexpensive, and possibly just an interim solution is for one of the Ryobi motion sensing alarms. I purchased one for my shed a few years back. Unfortunately, when I looked at this today it showed that it is discontinued (
Ryobi Tek4 4-Volt Motion Sensing Alarm RP4300-DISCONTINUED-RP4300 at The Home Depot). However, your local Home Depot may still have some in stock. Granted, this is not going to alert your neighbors to the alarm, though it will (hopefully) scare off any potential unwanted visitors. If nothing else, it could serve as a temporary measure until you obtain a 'true' alarm system... plus, it might allow you to sleep feeling a little bit safer.
On a side note, most of my father's family lived in Chattanooga/East Ridge. I grew up on Sand Mountain and most of our shopping was done in Chattanooga. My older brother and his friends often cruised up and down Brainerd Road endlessly on the weekends... this was back in the early 80's. I wonder if that still goes on there.