First do everything possible to make your home an unattractive target: Lighting, dogs, good deadbolts with plate screws that go deep.
After that, I'd personally grab the Mini 14 over the 870 if all else failed. However, I would probably choose something other than ball ammo and I would make sure the rifle is reliable with it.
This will probably re-launch another carbine vs. shotgun debate. I've thought through it carefully, done some research, and decided the carbine is a better choice for me. Others will probably disagree. They aren't going to change my mind and I doubt I'll change theirs.