It's probably already been said in this thread, but there is no round that will reliably stop a bad guy and yet not go through many layers of drywall, for a shotgun or otherwise. I'm sorry but it just doesn't exist. People are made of tougher stuff than drywall and so in order to penetrate deep enough into a bad guy to reach vital organs, which needs to be done to stop someone, it also must be able to penetrate many, many layers of drywall.
Basic rule of thumb is to simply pick whatever is most effective and then when the time comes, be sure of your target and what's behind him/her. You could use birdshot which should only penetrate a few layers of drywall, but that absolutely will not reliably stop someone. There's a small chance it may stop them, but if you're worried about your safety, are you willing to leave it up to chance?
Use buck or slugs and be mindful of where you're shooting.