I'm also in the process of teaching the lady in my life how to shoot. So far she's fired a couple of 9mm pistols, my short-barreled AR in 5.56, a shorty AR in 9mm, my 10/22, and my Savage .17HMR.
Of the bunch, her favorites are the 9mm AR and the Savage. She loves the short range accuracy of the savage and it's high magnification scope. She says the 9mm AR "feels like it was made just for her".
From what I've seen, she finds firearms that are relatively light and have a shorter LOP to be easier to handle and fire accurately. This doesn't surprise me, given her stature.
After only a little bit of instruction, she was grouping reasonably with the AR over iron sights at 25 meters. I'm anticipating that once I have a 9mm AR of my own built with an Eotech or Aimpoint built, she'll find that to be an excellent carbine for her.
I agree that a shotgun is in general a more effective personal defence weapon than a pistol caliber carbine. But, I'm also a firm believer that a firearm that's less than ideal in the hands of someone that's proficient with it is far more effective than the ideal firearm in the hands of someone that can't hit anything and is scared of the recoil and muzzle blast.
You may also find that a shotgun with just a bead sight is difficult for a novice to shoot effectively. When I built up my 10/22 to be easy to learn on, I put a reasonably ($130) priced Bushnell red dot sight on it. This makes it very easy for a novice to get the gun on target, and being able to see a positive result (putting rounds on target) quickly is a huge help in making shooting a positive experience for someone that's so-so on the idea to start with.
