I don't know.... this may start a flame war... but what the heck?
If you choose a shotgun, it really does not make much difference what type of shot you have loaded at across-the-room distances. The shot does not spread much, and will be devastatingly effective. Few people survive being shot with a shotgun at close range. A good pheasant load is a very effective home defense load (up to ~7 yards). Now if your target is 30 yards out, it matters a lot what you shoot. At that range 00 buck performs very well. Birdshot, not so much.
I'd steer clear of anything with too short a barrel. We had a little Rossi 20 ga./.22 switch barrel job. Nobody would shoot the shotgun a second time. Short barrel, light gun, really painful to shoot, even for an adult.
You might also re-think the handgun thing.
If you're under 21, you can't buy a handgun from a dealer, but it is legal to buy one from a private party if you're 18 or older (go figure). Anyway, that's the federal law most people come up against. You might also have some state laws that bar what you want to do.
At Harbor Freight, you can get a microwave oven size safe for $60. Pop your handgun into that, and open the door every night as you go to bed.
Sleep tight.