I see a lot of false information here and horrible suggestions.
NEVER EVER EVER suggest a semi auto pistol for someone that isn't very familiar with weapons, especially pistols.
IMO if I was getting a gun for home defense, I'd pick a Taurus Judge or Super Comanche. Both are pistols that shoot .45 Long Colt or .410 Shotgun shells. Very good choices for home defense.
The Taurus Judge is a 5-shot revolver, and fairly accurate. The Super Comanche is a single shot break open pistol. It's a little more powerful and extremely accurate, but if you miss your first shot, you may be screwed.

Taurus Judge

Super Comanche
I would suggest one of these pistols over a shotgun because they're smaller and easy to maintain.
If you want just a straight up pistol, you can't go wrong with a .357 magnum. I own many many guns, but the gun I keep at my ready is a Dan Wesson .357.
I would suggest avoiding automatic pistols, period. A revolver will never jam, a revolver has more power, a revolver is more accurate, and a revolver is easier to clean.
Cleaning is a big thing when it comes to guns. After you shoot your guns you should always clean them, otherwise the barrels will begin to rust inside, your gun will lose it's accuracy, and eventually become completely useless.
This information is coming from someone who's been around guns since birth, and shot their first gun at age 4.