What shotgun would you want to use to defend yourself at home with?
That would be one way to approach it, but running a shotgun in 3 Gun is about loading quickly while moving and managing your ammo (bird, buck and slugs) for the course of fire. Not quite the same as home defense. I have yet to see a dark house/low light course of fire for shotgun, unlike rifle and pistol.
Here are the Benellis I am currently running for 3 Gun, L – R, 24” Open (9+2), 22” limited (8+1), 18” limited (7+2)
My home defense shotgun is a Remington 870 18” cylinder bore, with Trijicon night sights and a weapon mounted flashlight.