Since I can safely assume that you already own an example of all three weapons, the one you choose for home defense really depends on your situation, and in particular, the design and location of your home.

If you live in a more rural area with a decent amount of land around you, I would choose the rifle.  You're likely to be farther away from external help, and you need all of the defensive power you can get.  And this is a situation where you *could* end up taking defensive shots at longer distances.

In a suburban or urban area, you are probably better off with a pistol, because any shooting you do will likely be at closer ranges, and it WILL be easier to move around, grab the phone, open doors, turn on lights, or whatever with a free hand.

If I didn't have or want to use a pistol for some reason, I would probably choose a pistol-caliber carbine over a shotgun just for the control factor (i.e., mild recoil) and faster follow-up shots.  They're ususally shorter and handier than a shotgun too.  I'm talking M1 Carbine, Marlin Camp Carbine, Ruger PC-9, and so forth.

[My Camp 45 was used as a loner "home defense" gun before we moved my grandmother out of her crack-infested neighborhood a year after my grandfather died (he refused to leave his home).  The family members that stayed their with her on an alternating schedule would not have been effective with a pistol (no experience/training), but could point and aim the carbine decently enough to be effective at short ranges.  Plus, the bolt was easy to work for the women, and the manual of arms was simple enough.]

While most of [b]us[/b] (gun enthusiests) could be effective *enough* with a shotgun, it has too many negatives to be a first choice when acting as a "lone operator."  They're long, heavy, have large, bulky ammo, low ammo capacity, are slow to reload or unload, and the multiple projectiles risk a lot more collateral damage (you're responsible for every pellet!).

-Troy