Lots of theories on what is best for various situations most of which boil down to personal preference. For a general home defense gun which may have to be used by women or children in an emergency I lean towards a youth 20 gauge automatic shotgun. No precision aiming needed, not too much felt recoil, excellent availability
The shot spread at house distances will not exceed the size of your fist. You can add that dont need to aim a shotgun much to the pile of myths too. They need as much aiming as any other long gun.
The old rule of thumb is 1" spread per yard of travel. So at 1 to 7 yards that gives you maybe a 2" to 8" wide pattern - that's not exactly "just point it at that end of the room and pull the trigger" spread. Testing by some sources suggests actual spread is only 1/3 to 1/2 that rate. Personally, I know my Mossberg 500 (12 GA) spreads bird shot (#6 or #8) to about a dinner plate sized pattern at 15 to 16 yards. Rifled slugs obviously are single projectiles that must be aimed, and even the #1 buck I've got in there (alternated with slugs) does not spread like the bird shot. Hence, if I ever have to use it, I plan on aiming fairly well. I don't want to incapacitate a limb, I want to knock down anyone that needs it and take them out of the fight immediately.
I lean towards a youth 20 gauge automatic shotgun. No precision aiming needed, not too much felt recoil, excellent availability
Studies have shown that there is very little shot pattern spread over the length of the room in an average size house. Might want to think about using slugs.