Frankly, for home defense, a load of buckshot center mass from a 20ga is going to "deter" a bad guy just as well as a 12ga. Buckshot, slugs, shot, you name it, if it's available for 12ga, then it's available for 20ga.
I'm a fan of 12ga, and a BIG fan of the Benelli Supernova. The only downside of a 12ga is the size/length of the weapon, as it's very hard to find "youth model" 12ga's, because most youth models are 20ga.
It seems like you're all over the place right now. Do you want a weapon for home defense, or do you want a hunting weapon? Then further, do you want an upland shotgun, a turkey gun, goose-gun, deer slugger, etc etc? Sure, indy cars, stock cars, funny cars, and drag racers are all "race cars", but they all have very specific purposes. I have 5 Benelli Supernova 12ga's, and all of them have different specialties, coyotes upland game, turkey, and 3-gun (back-up for my Benelli M4).
Get a little better picture of what you're wanting out of the weapon, then it'll be much easier to point you in the right direction.