No. 4 or even No. 6 shot will do as well as any, put more pellets out there than buck or slug loads, and shot that misses will do less damage to the walls, book shelves and other things in the house.
But there are two common misconceptions about shotguns for HD. One is that a shotgun unleashes a "cloud of shot that will fill a room and you can't miss" any BG in it. Shot spreads about 1" per yard of range, so across a 15 foot room, you get only about a 5" spread. Better aim.
The second is that persons in another room will be safe from over-penetration with a shotgun, even with buckshot. In fact at short range (say ten feet), even No. 7 shot (a common small game choice) will blow a big hole in most drywall and do serious harm to anyone behind it. Again, better aim.
Jim