Hi, tiggerbaby, and welcome to THR.
I'm afraid I can't offer you a whole lot of encouragement on that armor piercing thing either, Shotguns tend to be pretty low velocity firearms, given their relatively large bores, and high velocity is generally needed for anti-armor work. If it helps any, you aren't likely to really need to shoot through armor under normal circumstances, and if you are ever confronted with a body-armor wearing assailant, the impact of properly selected and accurately delivered shotgun projectiles on that body armor is going to be... disconcerting... at the very least.
Recoil is indeed the single biggest issue with shotguns as a defensive weapon. But there are ways to overcome that, often enough. My wife is your average university professor, in her early 60s, 5'4" tall, about 125 pounds. She can handle a 12 gauge just fine.
The 'secrets' to that are proper gun fit, a premium recoil pad and training and practice in proper technique. The "house guns" here are all Remington 870 pumps, first for commonality and second because good used 870s are relatively plentiful and pretty inexpensive. We have several because they are secreted in hidey holes in different places in the house. That way neither one of us can be cut off from a shotgun by someone with ill intent entering either doors or windows. We both carry pocket pistols at home but there's nothing like a long gun when you really need a gun. We have no children in the home, BTW, and when we both leave the house the guns are put back in the safe.
From a hardware standpoint, the 870s here have stocks that were shortened to 12.5" length of pull, including a KickEez or LimbSaver recoil pad. The current Remington R3 pad is a premium pad, BTW, and does not need an upgrade- just a refit if the stock needs shortening.
Most shotgun stocks are too long from the factory for many shooters. It's easier to use a shotgun stocked too short than one that is too long- I'm 6'3" and wear a 37" sleeve, and have no trouble using the abbreviated Remingtons here. The only difference in form is keeping the shooting hand's thumb safely parked on the trigger finger knuckle to avoid nose-bashing under recoil.
Barrels are 18- 20", some with bead sights, some with rifle type sights. It doesn't matter that much IMHO what kind of sights are on a defensive shotgun, it's a shooter preference sort of thing. There are no magazine extensions- my wife says they add too much weight out front ahead of the support hand and make the gun muzzle heavy and harder to hold up.
Each gun has a standard field length (9" IIRC) forearm as opposed to the shorter 'law enforcement' length- that makes it easier for shorter arms to reach and operate without over-extending. The guns have 4-shot Sidesaddles mounted on the receiver to hold extra ammo. In our case the Sidesaddles hold slugs, while the magazines are loaded with 00 buckshot. With magazines loaded one round short and chambers empty, it is easy to load a slug first if that happens to be called for.
Each gun has a simple light rail mounted to a ring that goes under the magazine cap, to provide a mount for a pistol type rail mounted light (see
http://www.streamlight-flashlights.com/69906.html for pic). IMHO a defensive shotgun needs to have everything mounted on it you might need when you pick it up, and that includes a white light source and extra ammo. I think the new generaion LED rail lights are better for use on shotguns- shotgun recoil tends to be hard on filament type bulbs.
If a 12 gauge seems too much for you, I suggest a good gas-operated semiauto in 20 gauge might work better. Not a pump- 20 gauge guns tend to be lighter overall in weight than 12s, and there is a lot narrower selection of loads available in 20 gauge than in 12. The combination of a gun that weighs less and a heavier load means more felt recoil.
The variety of reduced recoil 12 gauge defensive loads available is very wide, and reduced recoil 12 gauge loads in a slightly heavier 12 gauge pump will kick less than most 20 gauge guns. Gun fit is still critical though, even with a 20 ga. gas operated semiauto. The down side to semiautos is that they tend to be about twice as expensive as a pump.
I suggest to women as a matter of course that they seek out other women for firearms training. I think it just works better. Other folks disagree- they're as entitled to their opinion as I am to mine, I think. I suggest you spend some time at sites like
http://www.womenandguns.com/ and
http://www.corneredcat.com/ . There are a lot of women out there who enjoy the shooting sports, and a lot who take defending themselves and their families as a matter of course. It might help to 'get to know' some of them, even if only electronically.
If you're a beginner, first you have to learn to shoot, then you have to learn to FIGHT with a shotgun. The NRA has instructors in many areas who offer basic firearms classes, including shotgun. I suggest taking the NRA Personal Protection In The Home class as a starting point for the transition from shooting to fighting- see
http://www.nrahq.org/education/training/basictraining.asp to find out if there is an instructor near you teaching these classes.
Best wishes, and Stay Safe,
lpl/nc