Been thinking about this since I read this at James' place. It's not a new idea, and it's a good one. I've told a few people who asked "Look, unless you're set on a handgun or have some particular reason to go with one, for home protection get a shotgun". If they live in a rural area I might lean toward a rifle, but the principles stay the same:
1. It's easier to shoot accurately with a long gun.
2. It's easier to teach someone to shoot accurately(generally) with a long gun, and
3. No handgun ever made can match the close-range stopping power of a shotgun. Period.
And it's not a general recomendation, but in very close quarters a shotgun or rifle can be thrust forward to ram the muzzle into someone, or you can butt-stroke them. NOT things I would recommend, but in a pinch it'll work. The muzzle ain't no bayonet, but all the force of your highly stressed body hitting someone in an area less than an inch square...
Right now, concentrating on shotguns, if someone cannot handle/won't work past the recoil of a 12 guage(and even with reduced recoil loads it can be too much for some), a 20 guage will do just fine; we're talking about across the room or down the hall ranges here, the bad guy won't know the difference. As to shot? The scattergun I keep in the house is stuffed with Hornady TAP 00 buckshot; it's a reduced-recoil load of 8 pellets instead of the normal 9 and it groups tighter out of my gun than anything else I've tried. And the recoil is noticably lighter. If I could find a reduced-recoil #4 buck load I'd give it a try; more pellets=more weight hitting the bad guy and even less chance of shooting through a wall to a neighbors house than 00. If you're really worried about overpenetration, go to a heavy birdshot; it'll probably have lighter recoil than most buckshot loads, too. And again, at the ranges we're talking about, the bad guy shouldn't know the difference.
Generally I'd recommend buck, but I do have to note that Peter Capstick once wrote of the lioness who charged him when he was out bird hunting, and all he has was, as I recall, some #8 field loads. He busted her in the chops at about twenty feet(can't find the piece right now) and reported that it did a truly fine job on her head and dropped her dead at his feet. If it'll kill a lion, it'll take out a man.
As has been written, if you decide on a shotgun get several different types of shells and try them out, preferably from a rest at a paper target; find out what actually hits where you're aiming and gives the most appropriate pattern. I like the TAP loads partly because they produce a tight pattern at home-defense ranges; I've known other people who used loads that spread out as much as possible, figuring that gave them a better chance at getting a piece of a moving bad guy in the house at night. I knew one guy who made up his own loads using a 'spreader' wad, at fifteen feet the 9 shot were in a pattern two feet across.
And, unless there's some special reason for it, DO NOT USE SLUGS! In a 12-guage most slugs are 7/8 ounce to 1 ounce in weight, overpenetration is what you WILL get. I read a while back of a police department deciding to test this on some houses scheduled to be torn down. They found that a standard 7/8 oz slug fired from the curb, unless it hit the water heater or something else heavy and solid, would go through the entire house and come out the other side with enough energy left to penetrate at least the outer wall of the next house.
If anyone out there is wondering about my expertise, I'm very happy to inform you that I've never shot anybody with anything; I'm going by what I've read and been told by people who've extensively tested it and, in some cases, used it for real. Generally speaking, what I've read has been split between 00 and #4 buck as being best, with some votes for sizes in between. Like I say, I think a reduced-recoil #4 would be just the thing. Anarchangel once tried some Federal loads(no longer listed, dammit) that were reduced recoil with a mix of 00 and #4; he said it was great stuff.
One last thing: as a bugout gun, a shotgun has the wonderful versatility of using a mix of ammo. You could use buckshot in/around the house, but for longer ranges you can keep some good slugs handy; with decent sights and practice many scatterguns will give accuracy close to or equal to many rifles out to 100 yards or so with slugs they like.
My opinion, for what it's worth.
Note: in his book Last Horizons Capstick has an article he wrote for Guns & Ammo magazine in 1976 on buckshot for hunting; there's a good chance your library has it or can get it, and it's well worth reading.