I'll chime in, and consider myself somewhat an expert in the subject.
Back when Ohio first passed our CCW law, I quickly signed up for a class so I could get my license. In class, there were many "trophy wives" who obviously had never even handled a gun before. They were extremely nervous and would visibly shake from being nervous on the range.
I saw an opportunity , and started a small business to educate people on firearms and firearm safety. I started by holding clinics for women at local golf clubs. 7:00PM - 9:30PM at the clubhouse, then offered in-home sessions for anyone interested. These sessions were all about how to handle a gun, nomenclature, and gun safety.
I also offered to escort people to the range, and practice with my firearms, or something they want to rent from the range.
Full size shotguns were too big and heavy in at least 80% of the ladies I taught. And of the 20% who were able to shoulder a shotgun, about half didn't like the recoil. And if you think dropping down to a 20ga helps, it really doesn't.
I would suggest finding a handgun that she could carry concealed if legal in your state. One gun can serve both home defense and CCW. The added benefit is being familiar with your one weapon, rather than 2 different ones.
Semi-auto pistols are way more complicated than revolvers. With a revolver, you pull the trigger... no messing with slides, safety switches, mag releases, etc. The only down side to a revolver is width and limited number of rounds. But the chance she will ever need more than 5 shots is remote.
Don't start with a concealed carry piece. The sharp recoil associated with a small lightweight pistol is scary to most women. Start with a full size revolver, probably in .38 special. The recoil is somewhat tame. Then, move either to larger caliber, or smaller gun.
Honestly, with bullet design these days, there is nothing wrong with .380 for personal defense. However, larger caliber is almost always better. Just start her off with a small caliber and let her progress from there.