A pump shotgun is a great choice. A little handheld, 5 +1 round capacity shotgun is a poor choice. Get a full size shotgun that you can shoulder, not a gimmicky Tac-13. Also, if someone is in your house, they should never hear you chambering a round (pump slide).
Only accurate thing about this is they shouldnt hear you racking a round.
You think an extra 2rds is gonna make any difference? I've been shooting since I was 7, boy scouts since kindergarten, hunting rabbit since 8/9, deer and pheasant since 10, so on and so on...
I can handle a tac-14/13 just as well as a shouldered 8rd "tact"870/500 w/a pistol grip.
However I can handle an AR even better, and follow-up/dbl tap rounds are much, much easier with an AR. Had a gun in my hands for 30yrs now, I know what's behind when I pull a trigger, and an easily maneuverable AR-15 pistol that's shoulder-width a sub 10 inch barrel, is just fine... So long as it has a lite/strobe. Don't even need a red-dot/aimpoint for home defense, so long as you can see the front post.
*Should read "AR15 pistol that's "shouldered" (w/a brace)