I agree and would like to offer alittle more. If you are not use to a firearm, as you seem to imply, PLEASE Don't think just because you have a firearm you are the PROTECTOR. That will get you and yours KILLED. Especially if it is as bad as you say it is in this area. Get somewhere and get some training in personal protection and self defense as neccessary? I teach alot of firsttime shooters how to shoot a firearm in differnet situations, including Self Defense(which by the way is the last resort to kill another person). Find a local teacher and or gun shop that can help you out. Again we aren't being hard A****, but want you to learn the whole story? JMOWell, first off, Welcome to the Forum.
I don't want you to get the wrong first impression, the guys here are all really good about helping new folks out, but your post is going to get torn apart a bit. Don't take offense, the guys are just going to try and help you out by pointing out some flaws in your theory.
Okay, if you have never fired a weapon before - you need to seriously reconsider these choices. You need to go to a range, rent a few pistols, and maybe a couple of .22 rifles, and get a feel for what fits you - not what you THINK is going to fit.
Shotguns are considered long guns, and as such, probably have to have a minimum of a 16" barrel where you live. Check your local laws, but that is pretty standard. Now, add the action and a decent stock and you are looking at, probably, close to 30 inches of plastic and steel in your hands.
Take a 2 x 4, or a broom handle, or whatever you have available, that is around 30" and try to move from room to room, through doorways, and around corners with that thing in front of you. Not the easiest, nor the safest choice.
Also, buckshot will do serious damage to a human, but it will also over penetrate and could smash through drywall within the house itself. You could be putting your significant other, or your neighbors, at risk..... and that comes with liability.
The mini-14 is a horrible choice because it's a piece of crap rifle that has more drawbacks than advantages, but a .223 rifle round will DEFINITELY go through walls and easily over penetrate, see liability above.
The first thing I would suggest is making your home less of a target. Bright lights on motion sensors, a dog if you can have one where you live, an alarm sign, even if you don't have the service, as a deterent. Cut 2 x 2's to put in your sliding windows and have outside lights, and inside lights, on during the night.
After the place is more of a fortress and you have actually spent some time at a range and are more familiar with weapons in general:
I would suggest a good, double action, pistol in greater than a 9mm for your first choice. Something that both you, and the female unit, are comfortable with. A pistol will clear a house much faster than a short gun, or a rifle, and it will come to bear on a target, God forbid if you ever have to do it, faster than any long gun.
With the right rounds, you can insure massive wound trauma without the chance of over penetration....