I'm sorry to hear that your new house is already showing signs of vandalism. I'd get cameras up on that place asap.
Effective security is all about layers, failure compartmentalization, and slowing the advance of the adversary (elastic defense / defense in depth).
Install exterior lights, lots of them, and illuminate them 24/7. Add bright flood lights on motion sensors as well (pointed toward your home, not neighbors). Don't give any trespasser the privacy to try and make entry.
Establish a full exterior perimeter around your home, with a focus on all ingress/egress points (windows, doors), with a set of high resolution color cameras that either record 24/7, or record when motion is detected. It is best if you can have each camera looking at where the next camera is mounted, which will catch anyone tampering with the cameras themselves. Put up signs that say 24 hr video surveillance.
Install a home security system w/ monitoring. amRam is right about response times, but this is another layer that will aid when you can't sit around monitoring your camera feeds all day. Everything helps. Get glass break sensors, motion sensors, and entry sensors on all your windows and doors. You can put panic buttons around your home as well. Put up signs saying you have a home alarm system, put stickers on windows and doors as well.
Get a double strike plate for your door jam. It reinforces the weakest part of the door jam making it more difficult (not impossible) to kick in.
Put 3m security film on your windows. Again, it doesn't make it impossible to break it, but a half a dozen noisy whacks with a hammer, and a would be intruder still hasn't made entry, they're probably going to give up. If not, the alarm should be going off by that time anyway.
Get a dog. Big, little, young, old. It doesn't really matter as long as they go ape shit when someone comes to the door. If you do want a dog that can physically defend you from an intruder, then consider that as well.
Get a driveway alarm, or something else that will create an audible chime or alert in your home when someone pulls a car into the driveway.
And finally, arm yourself. If someone manages to make it past all of the previous layers, and into your domain, you can probably assume they're a persistent and dangerous enough threat to warrant lethal self defense.
Create an emergency response plan for when someone does break in. Plan where you'll go to make an escape, as well as where you might want to hide call police, or defend a position. Practice and drill for that plan, especially if you live with others, or are protecting your family.