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+2 on start with a .22.
Last year I took my 30 year old daughter to the range for what turned out to be the first time she had shot a handgun. I had several pistols that day

Ruger MkII .22LR
Seecamp .32
Sig P238 380
Ruger LCP .380
Star 9mm
1911 .45 ACP

Unfortunately the .22 would not work that day.
She shot a couple of the others and didn't want anymore due to recoil.
Luckily someone had a beat-up .22 revolver we borrowed, and she liked that OK.

Next time we went I packed a bunch of .22s, including a Henry lever gun.
She enjoyed those a lot.
I have a Smith K98 revolver and some target loads for her next step up, then probably a 9mm 1911

So let her have fun with a .22. She'll tell you when she wants to try something bigger.