It seems some knowledgable people are saying tight patterns are best, but the OP was talking about household distance.
While I agree uniform patterns (even spacing between pellets) are good, I'm not sure I buy into tight patterns at HD distance. For instance, Federal has a 00 Buck load that stays within the wad until it strikes its target, would you use that for HD? It is a bit extreme but its the same idea.
For any given distance I'd think evenly spaced COMish sized patterns (or slightly smaller than COM) are best.
PS: I'd probably use 00 over #4, because of stories like rcmodels and because he's right about the police choosing that load and why. I do hypothesize #4 would be darn perfect for stuff like yotes or even big coons, pattern willing.
Edited to add: Forget where I've read it but a credible source said #1 would actually be optimal, it's just 00 is much more available. Take that for what its worth though, I dont want to be responsible for perpetuating internet misinformation.
Heres the kicker, I havent even bought my shotgun yet! -.-
Anyway, Looking forward to more discussion.