Alex, you are right there in that lovely grey area. That said, you sound rich. Adopt me, and pay for my Masters or Med School?
Joking aside, I would ask myself where I am likely to confront a BG. Would it be as they were rising the steps, around a corner, up close, or at a distance? Decide where you are likely to find yourself fighting, and that can determine your gun.
I did the same thing in my current residence, and because of the way things are, I think a shotgun would be better. (That said, I simply haven't gotten one yet, which is why an AR is my current go-to longarm.)