If your going to use a shotgun, I would suggest loading #4 buck. 00 and 000 buckshot have a tendency to overpenetrate walls.
The only problem I have with handguns is people only fire a handful of rounds every few months from them. If you don't train properly, then a handgun is almost worthless. I've seen more people fail to put rounds on target in a high dress situation with a handgun than any other type of firearm.
People usually find they are more accurate with a ar15 with minimal training. But you go back into overpenetration again, so make sure to use frangible rounds for indoor scenarios.
As with all thing defense related, train with what you have and feel most comfortable with. If you haven't practiced clearing your home with whatever firearm you've chosen I recommend you do so.
I would suggest using all three firearms to do so, you may be surprised which one works best for you.