Given OP's options, I join many in preferring .32 over .22, while acknowledging the advantages in hi-volume practice with a .22. I also agree with the "get her what she likes" school of thought!!!
In my family, we found the .38 S&W to be a wonderful compromise for my wife and daughters, matching up a 33-1 4" bbl house gun with a 32-1 2" bbl carry/car gun for each of them & for me

Report & recoil similar to a .32SWL Mod 30-1 they had liked, but drills a larger hole.
Mild factory ammo available at my LGS, Cabela's, Bass Pro, and usually several on-line sites. Of course, much easier, cheaper & more versatile if you handload. For my girls, I've decided on a .358 hard cast 148g wadcutter, at factory duplicate .38S&W vel of about 700.
I won't tell you what I load mine with, as it might cause a riot on the forum. Hint: Ken Waters's "Pet Loads" article some years back lays out some loads that would really surprise you, e.g. 140g JHP at 984 fps in a 4" solid-frame gun. Now, look at factory ballistics on a 2" .38 SPL +P Speer 135g GDHP-SB, and guess what's in my 33-1? (This bullet expands fully at 860, according to Speer.)
Loading the 38S&W "long"--to lengths approximating 38 SPL COL's--I use Lee 2nd Ed. data to move a 148g LWC at 800 in 2" and 900 in 4". As always, YMMV with such hot loads, and I use them sparingly in modern steel solid-frame guns--NOT NOW & NEVER, EVER in old top-breaks!!! Work up, be careful, etc etc before adopting my approach.
Even published data in Speer 13, Lyman 49, and Lee 2nd gives safe, pressure-tested loads with standard 158g lead bullets that approximate 38SPL standard-pressure ammo, and recipes for 200g bullets at low 600's are plentiful, duplicating the old Super Police and British Mk. I service ammo. The 38S&W cartridge can do a LOT in the right gun, while offering much more sedate options for the recoil-sensitive that are more effective than smaller calibers. Hand loading is a snap, and .358 component bullets work fine in my S&W's, which have a groove diameter of .359.
Finally, these guns weigh 17-18 ozs. and are much easier to handle than modern 10-12 oz. guns in 38SPL.