1. Security system will give you some peace of mind, but if you're feeling paranoid, you might be better off with a therapist (and an alarm system). It might just be adjustment issue that will go away over time.
2. You can get ADT, etc. Just be aware that they'll get you to sign 3+yr multi-year contracts (that's where the money is) for $40+ per month.
3. Most security systems will cost $1200+ to install. ADT or some big companies will offer "packages" but it'll always be cover less than what you'd like (only 4 windows, 2 doors, etc. when you have 15 windows and 4 doors, etc..
4. You can do it yourself. Some home installation kits will alert you only, but some work as full security systems with everything. (
http://simplisafe.com/build-my-system)
5. Security systems are deterrents. If someone really wants to invade, no dinky little alarm's gonna stop them. Keep your house unattractive to thieves by keeping windows/doors clear of any brush/trees. Keep a house timer to keep the lights on when you're not home. Don't show any expensive stuff that can be seen from outside. Etc. etc. Most of the deterrence is the alarm company sign in the front lawn.
6. Best alarm? Get a dog. Having a barking dog is the best deterrent you can get outside of a 24/7 bodyguard