My opinion based on teaching my wife to shoot well enough to pass the new and improved USAF small arms qualification course before she deployed...
Get a fairly large frame gun, and go with something like 9mm. You can go to .40 if she's strong enough and if it's a big gun like the beretta auto the military uses. I taught my wife with my beretta .40 (the exact same gun as the USAF uses but in .40 instead of 9mm), so when she qualified in the 9mm she already knew how to point the thing, take it apart, clean it, and put it back together again.
If she has smallish hands or isn't terribly strong, you can find a smaller gun but still go with a round no more powerful than 9mm. .38 is fine since you can simply buy weak or hot rounds as desired, but I think 9mm ammo might be slightly cheaper and more suitable for an auto if that's what you want.
Since this will be a hobby, she might appreciate a DA/SA auto so she can learn to excel shooting both in DA and SA. Again, the beretta was a fine teaching weapon for this since it has a foolproof decocking lever. Those DA only autos... Might as well get a revolver with the hammer horn filed off since the revolver would have less parts to break.
But again, I'd suggest a medium to large frame gun, maybe a DA/SA auto, in 9mm or no higher than .40. Plentiful cheap ammo and being able to fire it for an hour without wrecking her wrists ought to be a goal.
Alternative suggestion - Get a high quality .22 auto or revolver. She can shoot it all day for a couple of bucks, and it won't hurt her wrists or wreck her hearing. Then she can focus on tack-driving accuracy (if she cares). But it should be a quality gun, not some piece of junk that won't let her show improvement.
