@2Fast2Curious, booby traps so you know when he enters your property. They make a alarm for driveways that is a motion sensor, sounds a alarm in your house when someone comes into your driveway. Can be setup anywhere, small inconspicuous, wireless, and he won't hear alarm. I know someone who uses one to alert him to deer in his garden, could be used for predator control also. $18 for this one; http://tinyurl.com/jd6m2zd
Or beer cans/soda cans with a few stones in them, stung to fishing line, setup throughout your yard, if you could hear it in your house. Or if you want to be cruel, boards with long nails in them, I bet you do hear the screaming in your house....
I don't think you have the right to shoot someone unless your life is in imminent danger, shooting someone for trespassing could get you a prison sentence depending on the circumstances. Even people that have shot burglars have ended up in jail.
For self protection, I wouldn't recommend a handgun unless it has a laser sight. Handguns are not easy to shoot accurately without A LOT of practice if you don't have the laser sight. And very inaccurate with their short barrels at anything not up close. Big bore hunting handguns are highly accurate even at long distance shots but kick like a mule.
Shotgun is a much better choice for home defense IMHO, and less likely someone is going to get hit with a stray bullet down the street, neighbors house, etc. 12ga kicks a lot, they do make reduced recoil shells though, 20ga kicks less and also there is reduced recoil shells available, .410 hardly kicks at all and is still very effective and the do make a few different style options defense buckshot rounds for them. I would recommend the actual shotgun in .410 but there is handguns available in .410, check out the Taurus Judge series.