I generally recommend a shotgun in the .410 size. Couple of good points, especally for a "family" type home.
1. It will put someone down HARD in close range, and in CQB it is ALL close range.
2. With bird shot, it will still put someone down HARD at close range....(see above) yet you don't have to worry about over penetration from one room to the next if you family is scattered throughout the house.
3. If you are not home and it needs to be used by someone with a slight body build, say a wife? It will be easier to for her to re-engage after firing a round.
4. Nothing is more intimidating to your standard bad guy than someone yelling "I have called the Police! I have a gun! *CLACK CLACK* Leave now!"
5. It is easier to aim than a pistol, especially at night, in the dark, when you are VERY stressed, and your family is at risk.
and the final one is...... IF you do use it, and IF you do get brought up on charges, having a big black Army Ranger Recon Seal Sniper looking shotgun makes it look like you were just waiting for the poor schmuck to break in so you could fill him with lead! A .410 will look like what it is. A shotgun, not the next bringer of death.
I would also recommend completing the NRA Personal Protection In The Home course. Not a big deal, but it is one more thing to throw down in case you do end up in court. You carry a fire arm to be prepared, well you need to be prepared for after you use it as well.