Regarding wall penetration, even small buckshot will sail through drywall very handily.
I'm fortunate, though, that the dividing walls between my townhome and my neighbors are core filled cement block, so I don't have to worry about over penetration. And, the exterior shell is brick clad.
I'm also single, so I don't need to worry about interior overpenetration. As long as I know where my dog is, I have clear fire lanes for whatever load I choose to use, but I still choose No. 4 buckshot as my primary load out with a 5 rounds of S&B 00 buck in a buttstock carrier.