As an avid gun owner, get a shotgun for home defense. If you want a pistol to shoot, or conceal carry then by all means get a pistol, but since your stating self defense for the home...shotgun. People always think pistols are easier to use than a shotgun when it comes to home defense and they can't be farther from the truth.
Think about what a shotgun puts out (a spread of shot) compared to a pistol (1 bullet). Shooting at a range is one thing, shooting at a person when your adrenaline is going a mile a minute is completely different. It's much harder and more dangerous to try and fire a pistol at someone in the house.
A .45 leaves the barrel at something like 850 fps, even a hydra shock round is around 500 and they can pass through quite a few objects if you miss. I used to load glazers which were used for air marshals to take on planes. A glazer round is a hollow, thin bullet with little shot (like a shotgun) in the tip of it plugged with a plastic cap. I did a little test one day and fired it at a wall in a house still being built (yes I had permission) and the glazers which are supposed to not be capable of wall penetration went right through the wall along with the hydra shocks.
The point is with all the adrenaline going through you your more likely to miss the target when they are in the house and send that bullet into another room where someone could be. You could even miss and that bullet could travel into the street and into another house and kill someone. A shotgun with #6 or #4 buckshot will not have that problem. Not only that you don't need to aim down any sights to bring the gun on target, just point the barrel toward them and pull the trigger.
I have 2 M14's, an AR15, 3 glocks (.45, .40 and compact .40 for CCW), an FN Five Seven, S&W .44, 10/22 rifle and the charger pistol, a Lee Enfield and a Mossberg 590. Out of all the weapons I own the shotgun sits next to the bed, the .45 is in the bugout bag and the rest are in the safe.
If your wife can't hold the shotgun you might look into a new one that is lighter. A remington 870 or Mossberg 500 can be found at Wally world for about $200. She doesn't need to shoulder it, hip holding it is fine when the intruder is in your house....she won't miss.
Also gun safety is very important as others have mentioned. Go to the range and practice, practice, practice! Make sure you store your gun out of reach of others and if you can't get a safe or small vault, use the gun lock the weapon comes with.
I see your in TX, if you want to get together sometime let me know. I would be more than happy to take you and your wife out to shoot some different weapons and to get a feel for them.