There are a lot more bells and whistles available for the Remington 870, like stocks, barrels, sight systemd, magazine extensions, etc. But, any shotgun, 12, 16, 20, The Cheney Special (28), or .410 in about any configuration will work, and work better with a shorter barrel. Ranges are close, and manuverability is extreemly important here.
A double or even a single would be fine also for HD.
Without hijacking the post, how you deploy your weapon depends totally on your situation, both tactical and residential. I use a layered defence here in rural Texas. Pistol, then shotgun, then rifle. My primary shotgun is a "dream come true for me" Benelli M1 Super 90. It will shoot a 4" group at 100 yards with Tactical slugs all day, so it replaces the rifle in the medium range arena. I still would never feel under armed with a decent 12 or 20 gauge pump shotgun, and securitysixshooter (I like your choice in revolver!) you have named a bunch of good ones. Just mu $.02