Don't take her to the gun store to see what she likes take her to the range and try some things live fire. Try a variety of calibers and a variety of gun.
I'm going to go 100% against an Airweight. I'm a 20 something year old guy and I even hate the recoil compared to a light 9mm. I can't imagine an arthritic 70 something year old woman liking it. Plus, I'd equate pulling the trigger on an airweight as just as difficult with a single finger than racking the slide on a full size glock with a single hand.
If it's just for home, maybe a 4" revolver or a service size auto with a bunch of grip tape on the side?
People who advise getting small lightweight guns for new shooters, or shooters with weak hands and arms, are doing a HUGE disservice to the new shooter.