S&W M&P .22. Then maybe the keltec pmr30 in .22 mag. Sometimes .22mag is easier to find.
My Wife likes my gsg 1911 22Lr. Its accurate down side is its a little cheaply made with plastic sights. I have never had problems with ammo selection some people say they do. I have ran about 600 rounds through mine and maybe two stovepipes which in my opinion is good practice because it is strictly a range gun.
Also don't forget about SIG line of .22 rimfires based on most of their full line pistols.
Ruger Mk ii hunter. Mk iii otherwise.
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I have the ATI version of this. Great pistol.
I love my Browning Buckmark for target shooting, but your best bet is taking her to a range that rents guns and having her see what she likes to shoot.
The only thing I don't like about the SR22 is the atrocious DA trigger pull. I took it out with my wife on a cold day and had to cock the gun for her.
I'll have to check out the M&P .22 compact. It seems to be the closest to what is now the standard in duty and carry guns.