START HER ON A .22!!!!!!!!!!!!!!!!
IF YOU SHOOT INDOORDS, HAVE HER WEAR EARPRO PLUS EARPLUGS.
I mad the mistake of not doing either one of those and it hasn't helped my wife want to shoot more. Learn from my mistakes. The first time I took her to the range, my friend had a .44 magnum rapid firing it indoors. He's kind of a wild man. We were in the bay right next to the wall. It was brutal and she didn't go back for years. Even I was like, dude...... Give me a headache why don't you.
And then once she did try again I had her shooting a .38 Colt Detective special with wadcutters and even that left a mark on her hand. HOW? I don't know. But it did.
Last time we went shot shot a .22 pistol, did very well and liked it. And she's shot a 10/22 before and did fine with that. But it's taken me years to undo the stupidity I did when I was young and wanted her to shoot with me. She had ear problems growing up so that made it worse. And even the last time we went, nobody was shooting and then when she went in to shoot with me, some guy started rapid firing his 9mm. And even that was kind of making her wince. I mostly shoot outdoors but that particular time we went indoors and it's just a lot louder in there. Of course you know that.
Anyways...... An AR isn't a bad choice either. I think it's easier to be accurate with them. But weight can be an issue and running it properly. Loading, etc.
Your wife might not be as dainty as mine though..... I'm just saying start slow and easy and let her decide if she wants to move up to more powerful.
Now my Mom, she shoots her .38 special BodyGuard pretty darn well, with very little practice. And isn't overly squeamish or dainty. She doesn't like to shoot a lot. But she's not overly scared of it. Except she prefers the snubby because when she had a M&P 9mm full size, she claimed it recoiled a lot and didn't like the brass bouncing off the walls indoors. It's funny because a lot of recoil in that gun, I don't see it. But it's her perception.