"Jagermeister," my suggestions are similar to those made by others but with some variation: My choices for a home defense firearm would be (1) a 20-bore pump-gun, say, a common Winchester or Remington, loaded with standard trap / skeet loads of no. 7-1/2 or 8 lead shot (At short range, density kills not shot size.), which provides one the power of an old black powder elephant gun at close range; or (2) if under the circumstances a handgun is absolutely needed, then my choice would be a revolver over any semi-automatic pistol, in .38 Special caliber, using 148 grain wadcutter bullets that have been turned bottom side up so the entire flat face of the bullet's base is presented, which full caliber (.356-.358, depending on the manufacturer and age of the handgun) projectile creates a more massive wound channel than the hollow point or soft point projectile that require more velocity to perform than the standard handgun cartridge is capable of producing, in order to match their 'billing' (or the weight of the bullet used is abnormally light for the caliber, so to achieve the needed velocity). If you do not hand-load, then a custom maker can provide you suitable cartridges, or perhaps a friend familiar with reloading can make the cartridges described above for you.
The suggestion of the 20-bore is made because guns of that bore are generally lighter and more maneuverable than larger bores. The gun's magazine can be loaded and then the slide and bolt drawn back until the carrier starts to pick up a cartridge, which allows for the bolt to remain open while stored for potential emergency use. When needed, the gun can be raised to shooting position, the slide simply pushed forward to chamber the cartridge, and the gun is then immediately ready to shoot. The gun can be stored where best accessible.
The revolver can be loaded and stored at the owner's discretion in a safe but readily accessible place. Shoot the firearm selected until proficient at the range anticipated.
We wish you every success in your search.
Regards,
Edwardian