Short barrel shotgun loaded with birdshot is a good choice for home defense i.e. 1 shot takedown, some allowance for poor aiming depending on distance, small chance of deadly penetration through outside walls, also a pump has the advantage of a sound like no other when cycled and may lead to a rapid exit of an intruder without shots fired.
All this. Add a cheap laser sight as well, and if the sight of a 12 gauge, the sound of the action as you rack in a shell, and the little red dot don't result in an immediate high-speed departure, shoot to kill because you're facing a very stoned and/or very dangerous intruder. A shorty pump with an extended magazine allows you to keep several shells loaded without the danger of accidental discharge as well as furnishing that lovely, bone-chilling sound of the action. Remember some things though:
Loaded guns are very dangerous around children.
Guns have to be almost instantly usable for effective home defense.
Never point at anything you're not willing to shoot.
A loaded weapon you're not willing to use is merely arming your intruder.
And even birdshot at close range will penetrate sheetrock and siding (maybe not brick or block, though I've seen it happen) just like a slug. Keep that in mind if you have to shoot. A friend had loaded a shotgun and forgotten to unload it; it later got knocked over and blew a fist-sized hole through the brick exterior.
My personal preference for shotguns is 7-1/2 or even 9 shot, which is more easily stopped and loses energy more quickly than larger shot and so is less dangerous to the neighbors. You can also get rat shot for handguns, but they typically have much less power than shotguns so fast-expanding, light JHP are probably a better bet.