Please don't buy one of the little shotgun revolvers..
A 12 ga shotgun is a good idea.. At home defense distances (like 5 yards) the pattern is about the size of your fist so you still have to aim the thing. Its not a point and shoot weapon like most believe..
If you have to rack the shotgun to load it, you brought and empty gun to a gun fight and that's a bad idea. Keep it loaded with one in the chamber with full power buckshot (2 3/4" shells), not birdshot, and propped up beside the bed. Also when you shoot a pump shotgun, its empty so rack the thing.
If someone breaks in your home, the only reason you should leave your room is if you have kids somewhere else in the house and that'd be to go get your kids and then you should all lock yourself in a room.
They can have whatever they want in the rest of the house, but the moment they decide to kick in the door where you and your family are, that's when I would stop them. I'm not SWAT or Special Forces & I'm not gonna go out and sweep the house and ultimately risk my life over a TV or laptop, but I WILL NOT let them near my family. While locked in the room, call 911 and I'd be screaming for them to leave.
You need to be extremely comfortable with whatever weapon you get because the moment you actually have to use it will be the most stressful time of your life, half asleep, with **** in your shorts, and you need to be able to still work it.
Also you need a weapons mounted light on whatever it is that you get. Can't shoot if you can't see. Gotta be able to identify who/what you are shooting. You don't wanna accidentally shoot your teenager sneaking in at 2 AM..
I think an AR15 is a better choice.