You can spend hours into days reading threads on this in the shotgun forum.
Living in a thin-walled condo apartment with a small child, I keep my 20 ga. with 6 or 7 1/2 birdshot. I think at <20', it'll hit like a slug but expend it's energy to not over penetrate.
By the way, the expression is "double-aught", aught being an old english way of saying 'zero'.