Action

There are two modes of gun action.

First there are those in which the user must ready the gun from one shot to the next (lever action, pump action, revolvers and more)

Second are those in which the gun readies itself (semi-automatic)

For a smaller, less-trained user (like a woman or child) I would strongly recommend a semi-automatic.

The action the gun uses to ready itself absorbs some of the energy and spreads the force over time, reducing the felt recoil.

Because the gun readies itself from one shot to the next, the user generally cannot interfere with the ready process.

However, because the gun is performing a complex task very rapidly it is possible for the gun to fail in various ways.

For example, it is possible for the shell that held the gunpowder for one round to fail to eject from the gun, blocking the next round from being loaded.

In contrast, manual action weapons will tend to have more recoil and (if operated correctly) are less likely to fail.

However, improper operation of manual action is a greater risk due to the greater responsibility placed on the user, and the failure rate of self-loading weapons is quite low.

Profile

Should you get a rifle, shotgun or handgun?

A long gun (rifle/shotgun) will be much easier to aim and control.

A handgun can be concealed and the smaller size makes it easier to maneuver in tight spaces.

Most importantly, a rifle or shotgun causes wounds in a different manner than a handgun and is far more powerful of a weapon as a result.

With handguns the body's natural elasticity (because it is mostly water) is able to absorb much of the energy and the bullet crushes a path through tissue.

In order to quickly stop a villian by handgun, the bullet must pass directly through the central nervous system or a major artery.

With long guns, enough force is delivered to overcome the elastic potential of the body and bullets can rupture entire areas of the body through which they pass.

In order to quickly stop a villain by long gun, the bullet must impact roughly in the vicinity of the central nervous system or major arteries.

Caliber

The final major category to consider is caliber.

Based on ballistic data, any handgun caliber of about 7.5mm or wider (eg 32 ACP, 380 ACP, 9mm, 10mm, 40 S&W, 45 ACP) will achieve the depth needed to present a lethal threat.

Any rifle caliber above 22LR will be fine (eg 223, 556, 30-06, etc etc)

Shotgun you're almost certainly going with 12 gauge due to availability, and then slugs are way too much and birdshots' not enough so it's got to be buck.

As to specific firearms, it depends somewhat on where in the world you are.

Some options to consider:

Glock 19 - Ultra-reliable and almost certainly the world's most popular 9mm handgun

Beretta 1301 - Semi-automatic shotgun

Benelli M4 - Semi-automatic shotgun

AR-15 in .556mm - Extremely light recoil, lightweight, and ammo is widely available in West/NATO regions

AK-47 (or AK74, etc) - High reliability and you may find the ammo more reliably in 3rd/Soviet world

If I had to pick one gun for home defense (which might be handled by less trained women or children) it would probably be the Beretta 1301 with 00 (double aught) buckshot.

I would also recommend you get a 22LR pistol / rifle (the same handgun / long gun choice as you made with your main gun)

This will be super low recoil and ammo is extremely cheap

This is a good training tool

However you do need to shoot your actual home defense gun from time to time to maintain competency