Let her choose both the cartridge and the pistol. If she chooses at least she will carry and use it
This ^^^^^
Take her to a range that rents a variety of guns and let her try them. Tell her that you're only going to object it she picks something unreliable or unsuitable; otherwise it is up to her.
It's also not a bad idea to find an instructor, preferably female, to give the basic instruction. Women often do better working with another woman.
