I'd say that unless you really need to concealed carry it, I'd stay away from handguns. They are underpowered (compared to long guns), sometimes are easier to make malfunction, and while the bullets may have less effect on flesh they tend to poke through multiple walls easier. Most of all, they are hard to shoot well.
They are pretty much the worst of all worlds.
I forget the exact numbers, but something on the order of 90% of handgun wounds are survived. The numbers don't quite reverse with long guns, but it's a lot different. Very few rifle or shotgun wounds are minor.
There is no reason to choose the least effective means to defend yourself unless you absolutely have to.
What handguns provide is convenience. They are easy to carry. I can't even say they are easier to store, because in a house, while a handgun can be dropped in the sock drawer, a long gun can be stored behind a dresser just as well.
The only other places they have an edge is if used in really close quarters use, and perhaps in that they make less noise than some long gun calibers. Noise might seem important if one had to shoot inside, but I've heard/read enough post-shooting interviews where they say they never even heard the gun to think it may not matter. As far as close quarters use goes, as an earlier poster said: If your wife is using a gun at home while you're gone, she's probably barricaded in a room and shooting towards the door from the farthest corner.
Street gunfights involving women tend to be really close distance. It's uncommon for there to be any distance separating the participants. Home defense is something else.
I can tell you right now what the gun shop will suggest:
"Get the little lady a small revolver"...and the shop's regular crowd will nod in agreement. They will say it's because revolvers are simple to operate. The implication is that other guns, especially semi auto pistols, are too complicated for women. Hmmm. I guess the guy saying that, and those agreeing, rose above the rocket science of a semi auto.
I haven't found a gun yet that was anywhere as difficult to use than a smart phone, computer, or the car my wife drives every day.
The statement of them being simpler is debatable too, in my opinion. A Glock, Smith & Wesson M&P, and Springfield Armory XD and several others are loaded and ready in fewer steps.
If you follow typical gunshot advice, you will get a small, short-barreled revolver (aka snubby or snub nose) in .38 Spl or .357 Mag (because a .357 Mag will shoot .38 Spl ammunition- and that will be a selling point the rocket scientist names).
What you will have there is one of the hardest guns to shoot passably, with muzzle blast, noise, and recoil out of proportion to it's effectiveness.
Can it be shot well? Yes, but anyone who can shoot one well can shoot almost any gun better.
I carry at least one handgun everyday. All day, everywhere possible. I get to an average of at least one class per year from a defensive shooting school or instructor; sometimes as many as four or five. I practice several times each week- this week I've been three times and will go at least once more. I shoot IDPA and IPSC (sort of "combat" pistol matches) and won the last IDPA match I shot, last month. I say this not to brag but as a setupto say this:
If I hear a window break in the middle of the night, the last type of firearm I'd grab would be a handgun. And among handguns, a snub revolver would be my next-to-last choice. (Last choice would be a small auto of .380 or smaller- often called a Mouse Gun- and probably what the gunshop will push after a snubby.)
I'd suggest a short rifle or shotgun, and lean towards the rifle.
My worry with a shotgun is that even the 20 gauge's recoil is enough to surprise a lot of first-time (or first time in a long time) shooters. It isn't helped when they hear or read everyone telling them it was chosen for its reduced recoil, which gets their mind set on it being a pop gun. Reactions can be anything from "Wow, that was more than I thought", to "Take this thing". It's rarely "That's not so bad. Let's do it again!".
If 20 gauge recoil is not a problem, then I'd suggest a Remington 1100 LT-20 Youth model. The Youth model has a shorter stock and barrel than standard. Most guns need a shorter stock to get into a really good recoil-absorbing stance (square-up to the target rather than the typical bladed fencing stance). Almost all makes could benefit from a shorter stock on a defensive shotgun.
The barrel on these is 21", which is longer than typical defensive shotguns' 18-20" barrels, but quite a bit shorter than the 28" barrel of the average hunting shotgun.
Overall, it's a slightly smaller gun than the 12 ga Remingtons.
The series has been made for 50 years, so a lot of people out there are familiar with them to help you if needed.
This Remington 1100 is a semiauto. Some people will say they aren't as reliable as a pump. Maybe fractionally so, but there are benefits that more than offset this in my opinion. The semi auto does the work, so there will be no chance of forgetting to pump the action. Don't laugh- I have seen it a lot. If she will be practicing with it a lot so running that pump is second nature, I wouldn't worry about it. If she won't- get a semiauto and forget about it. Also, a semi auto like this will sort of soften the recoil by spreading it out in the action cycling process. There is the same amount; it's just spread over a few milliseconds instead of getting it all right now. That little bit can make a difference with some people.
People like to say the racking sound of a pump shotgun is intimidating.
A) Someone was bold enough to enter someone else's house. Don't count on them being scared off by a noise, even that one. They've probably heard it before. If it works- OK, but don't count on it, and don't make a choice based on it.
B) Guns are for shooting, not scaring. Buy a halloween mask if you want to scare people. If you are face to face with them and feel the need to rack it for effect, you should probably be shooting them for effect.
One negative, BTW, to the 1100 LT-20 is that it is enough lighter than the 12 gauge 1100 that recoil may not feel that different. This is a subjective thing, and different people see this differently.
Choosing shotgun ammo for defense is another can of worms. As far as I know, 20 gauge buckshot is loaded with #2 Buck or #3 Buck instead of the larger 00 Buck usually used in 12 gauge.
Some people think birdshot (regular hunting loads) is best for a shotgun used for home defense. Their reasoning is reduced penetration if pellets hot Walsh instead of attackers. Birdshot still goes through walls, it just might not go through a many it travel as far after it does. Dint choose it thinking it's some magic projectile that can stop an enraged attacker dead in it's tracks while being unable to get through drywall.
Another point is that the smaller the shot, the more projectiles you are responsible for. And smaller pellets tend to deform easier, and deformed pellets take random paths. So while you get less penetration, you might have more wild pellets taking their own path.
Like I said- can of worms.
One last thing with shotguns:
You still have to aim.
Some like to say shotguns are great because of the "spread". They are not the "alley sweepers" some make them out to be. If you hang up a sheet of paper and blast it with buckshot at the distance you might have to shoot within your house, you will probably get a single hole about an inch in diameter, with maybe, just maybe, a hole or two just barely out of the big hole. Smaller shot will open up more, and definitely throw some wild flyers, but this is more random too, and not necessarily a plus.
If a 20 gauge is too much:
Shotguns smaller than 20 gauge usually means the .410. I've see too many rabbits get rolled by a .410 only to run on as if nothing happened. If I wouldn't take on a rabbit with one, I wouldn't arm my wife with one for defense. I'd take a .22- rifle or handgun- without hesitation before a .410.
That leaves rifles.
That's really my first choice.
I'll start here by saying I like the old GI M-1 Carbine. It's just too bad that originals cost an arm and a leg, and the modern-made copies can be so-so.
If you can get an original for a good price, I'd get it. Or if you're willing to pay what they are bringing, I think it will be worth it.
M-1 Carbines have really low recoil, and low muzzle blast. Noise isn't as bad as most rifles. They are short and light. Best of all, they are about as easy to handle as they come. Most kids can shoot one. They are easy to use one-handed, as if when needing to hold a flashlight. Even the loaded magazines are handy, because they are small enough to stick in a pocket, unlike most rifle magazines.
An oft-overlooked plus is the sight height above the barrel. Rifles like AR15s have a straight stock, which requires the sight to be placed high above the barrel to align with the eye. It works, but up close- like inside a house- this bore/sight offset means the bore is about 2.5" below the sights. In other words: You put the sights on a target at 10 feet, it will hit about 2.5" low. Sometimes 2.5" can make a difference between a hit that stops an attack and a glancing blow (or a miss). If the sights are close to the bore line, as on an M-1 Carbine, the offset is negligible.
I like AR15s, but there are so many makers out there that I wouldn't own half of them for a fun gun, let alone as a defensive gun. Thanks to that, I like buying known top quality brands. I like Colts, but they start at about $1100 and can be hard to find sometimes. Most people will say Colt costs too much and you can spend a lot less, but I've seen every single one of the less expensive brands fall down and die in classes. Most if their rifles may be fine, but i have seen too many that aren't. Instructors see every brand out there, and they see them used hard. That is why I take notice when every full-time instructor I know has a Colt.
But some people don't like their looks, don't want to spend that much, or can't find one.
Ruger Mini-14s are not my favorite rifle, but wouldn't be bad here. They look like a cross between a plain old rifle, an M-1 Carbine, and maybe a little AR influence. Although other calibers are available, but most are in .223/5.56mm like ARs. They have most advantges of the M-1 Carbine. Older ones had crummy sights, IMO, but that has improved on recent models.
Their downside is magazines. Any manufacture of magazine besides factory Ruger are to be avoided. Those can be had (finally, again) but cost more than AR mags.
The way the magazines latch into the Mini-14 is one of it's worst features, I think. They sort of hook in, then rock up to latch. It's based on its namesake, the M-14. It's not terribly difficult or anything, but isn't a very natural motion to most people. If it's a "Get the gun NOW!" moment, it could get bobbled or even wedged in wrong unless practiced.
A compromise of sorts, the best choice here might be a pistol caliber carbine (PCC). I usually don't like them except as fun guns, because, in short, I feel if one is be invonveniened with a rifle it should fire a rifle cartridge. A PCC loses the convenience of a handgun, yet won't come close to most rifles in performance. Yes, handgun ammo usually make a higher velocity when fired from a PCC's longer barrel, but it's not usually a huge change. Only when getting into the big Magnums does it really start to catch up.
But PCCs are a lot easier to shoot, and the skill is less perishable. I think if your wife were to get in the vague area of "OK to Competent" shooting a PCC, it could be stood in the corner and left for weeks at a time without those skills deteriorating drastically. I feel the handgun requires steady practice just to maintain competency. The shotgun needs more practice than most people give it, but it's a lot more forgiving than a handgun. Rifles are better yet. PCCs are not quite like learning to ride a bike, but shouldn't need very intense practice to be handy with.
Most PCCs are still probably lever actions in calibers like .357 or .44 Mag. Amazing shooting feats can be done with these, but I don't think they would be a good idea here. They require a fair amount of practice to load, operate, an shoot smoothly. Unloading, if that is an issue, can be kind of a pain.
A semi auto in 9mm, .40 S&W, or .45 ACP was what I had in mind.
The military style ones like semiauto versions of UZIs and Thompson SMGs are expensive, an in the case of the Thompson- heavy.
I was thinking more like the KelTec Sub 2000 or Betetta Storm. I think both are made in 9mm and .40 S&W. The 9mm would be cheaper to practice with, and the .40 is (possibly) more effective.
The Sub 2000 (or Sub2K to some) folds in half, so it might store easier in places like a drawer. They supposedly make versions that can use the magazine for Glocks, or S&Ws, or Berettas, or Sigs...but I've only seen them for Glock (mostly) or S&W (just one or two). They sell for maybe $400-450.
The Beretta Storm looks like a Ferrari (Beretta hired a designer- seriously) and uses magazines for the Beretta 92 (9mm) or 96 (.40) pistol.
All of those mags are readily available currently
There are other PCCs to consider (and attach one conversion unit for pistols) but those two make up the bulk of them. I've never owned one, but have seen several in use. They seem to work ok when decent magazines are used. For sone reason, people tend to use junky mags they wouldn't try in a pistol- maybe they think a carbine will be more forgiving.
So there are my suggestions.
-Avoid handguns unless you are really dedicated to it, and then, use it just to hold someone off while getting a rifle.
-If you want a shotgun, I'd suggest the Remington 1100 LT-20 Youth. Choices in semiauto, short-stocked. 20 gauges are out there, but get slim after that.
-I like M-1 Carbines for home use, but only original ones. Buy CorBon DPX ammo, test it to see that it functions, and use that.
-I like ARs too, but buy good stuff here. Don't save pennies.
-Pistol caliber carbines might have a place after all.