Ideal weapon is both. Right now my HD is a handgun, because my shotguns are on the mainland, but that'll change soon enough. The reason I say both is that shotguns are a two-handed affair, which is fine if you're all bunkered down in the back bedroom waiting for Mr. Bad Guy to come to you, but not so good if you're going to have to go down the hallway, across the living room, downstairs, scoop up a squirmy toddler, and retrace your steps.
Shotgun is good for barricade, handgun better for moving around the house to take care of other stuff.