I'm no expert in the field, but I did a lot of research to decide what I wanted. I wasn't going to pay for a monitoring company and the delays for them to call police makes it almost worthless anyway, compared to cost. What I wanted was a loud alarm that scared away intruders, and also alerted me that an alarm was tripped. I back it up with what amusa suggested, a wired cctv (hd-tvi) system that also alerts me by text. I receive alarm or camera motion and can instantly check to see what's going on.
I went with a Pisector alarm system. Take a look on Amazon, read the reviews. It did what I wanted and was reasonably priced. Wireless means I can set the sensors anywhere I need them. The only false alarms I have had are stupid people (me) caused, like forgetting I have an alarm system when I get up at 4am. Both intrusion alarm systems and security camera systems have become affordable for normal people and will do a good job without paying for professional monitoring. Do your research and decide which systems work best for you.