Actually, stay away from shotguns altogether. In the typical residence, in hallways, etc, there's just not enough room to maneuver. Plus, you typically would enter a room barrel first, which, given the length of a shotgun, would allow the bad guy to grab the barrel, wrest it out of your hands, etc.
There will also be semiauto weapons recommended. Again, stay away from these because for the novice/occasional shooter, the whole process of loading a magazine, pulling back the slide, safety/no safety, etc, can be kind of daunting for the novice/occasion shooter.
I also saw the Ruger GP100 revolver recommended. It's a 357 magnum and is an excellent choice. That revolver, or any quality revolver, is perfect for your circumstance. The average gunfight is over after about 3 shots, and the Ruger holds six. Once it's loaded, all you have to do is point and pull the trigger. No worrying about pumping the action, pulling back a slide, safety/no safety, etc.
Also, with a 357 magnum revolver you can practice with lesser expensive 38 special rounds, then load the gun with plus P 38s, or even 357 magnums, for home defense.
I strongly disagree with your comments on shotguns, but whole heartedly agree with your choice of handgun for the reasons stated.
1) Shotguns: Winchester makes several configurations of their Defender. It's a pump that has choice of stocks, an 18" barrel, 3" chamber, and holds 7 shots with 1 in the chamber. (It's good to leave the chamber empty and still have 6 in the hole so you make the unmistakable sound of racking the beast.) That's a gun which is easy to learn, aim/use, maintain, and will stop anybody without shooting up the neighborhood. Plus, you can buy a longer barrel and target shoot or hunt with it.
2) Pump vs semiauto: I've used a Browning 12 GA semiauto for 40 years and I can't tell you how many times I've had misfires or jams that required me to clear the chamber - but it's my skeet gun that I've used since I was 10, so I stuck with it - plus it's a Belgian Browning. I've had the same problems with my semiauto Colt .380 handgun, but never my S&W .44 revolver or pump Defender. Jams are frustrating when target practicing, but it's NOT what you want in an emergency. It's also more complicated to clean a semiauto. With a pump, as with a revolver, you don't have to worry about awkwardly clearing a misfire or jam. That's a BIG deal for a defensive weapon.