Corwin-Arms is bringing these into the country soon (within the next week or so)... Advantage over a short SxS is a slimmer profile, so it will slide between the headboard of your bed and the wall a lot more subtly, same could be said for behind your night-stand.
A short pump is better, overall, but given our storage laws, anything has to start off unloaded. Dropping a couple shells into a SxS or OU is faster than feeding a tube and racking, and on par (possible faster) than slapping in a mag and racking.
The above has ejectors (as opposed to extractors), so reloads can happen fast. But, realistically, the first shot or two is going to decide the issue. Even if there are multiple attackers, once one goes down, the rest tend to flee.
As for type of shot - well, that's the eternal debate. At "in the house" ranges pretty much anything - even #8 target loads - will have a very high degree of "f@ck sh!t up"... Even if it doesn't kill, getting slapped by a cloud of birdshot will seriously demotivate just about anyone.
#2 shot is about as heavy as I would personally want to go - I would want whatever I shot to be essentially harmless after passing through a sheet of drywall, if you head into the 00 zone, that might not be the case.
It's all theoretical. I have a kid in the house so I keep my boomsticks locked up, always. I'm more worried about her curious fingers than the extremely low odds of a home invader being an issue. And waking up in the middle of the night, shaking off the groggies, to deal with a home invader? Not conducive to really good split second decision making with a firearm.
But, it's your life, your choice. Whatever you decide to go with, make sure it also becomes your "Every Trip To the Range" gun, and go to the range. A lot.