A 12 ga. Coach gun is hard to beat, but its going to have to be something that is there, as in RIGHT there, since a home invasion is usually swift and violent.
No time to open a safe or dig a gun out of a closet.
On your person is the best bet, so that leans towards a carry gun which a 12 ga. is not.
That leaves an adequate caliber handgun that is on or close to you that you're proficient with.
The choices are limitless.