When my son started shooting big guns I got him his first Handi, then ordered a youth stock. The youth stock worked well with sights but when he went to a scope I had to cut down the original Monte Carlo stock to youth length. Was easy to do. When he got his 45-70, he put the youth stock on it. Then when he went to a scope he put a lace on leather riser to get his head up to the scope.
I would recommend a 30-06, 308, 7mm08, or the venerable old 45-70, if you go with a Handi. You reload so you can make them suitable for the quarry, and the old 45-70 with factory loads is not bad on recoil either, it just does not have the range the others do.
Just remember it is her gun, that seems to mean something to women. It's hers, not yours, and she will put forth more effort to do well. If it is your gun she will lose interest fast. For my wife's first rifle I got her a Marlin lever action carbine in .44 mag. To this day she shoots better with it, and it seems to be her favorite, over all the guns she owns now. The first thing I did when I bought her a gun was take it to a gunsmith and have the stock shortened. She actually goes a little shorter than a youth stock with her length of pull. She is only 4'11". Once a gun has been cut down for her there is no way I can shoot it comfortably, I'm 6'3". So get over getting something you can shoot if she loses interest, that will encourage her to lose interest. Get her something that is specifically hers. Do it right and you will have a hunting partner for life. My wife is the best hunting partner I have ever had. We work as a team when out hunting. I am colorblind, I look for movement, and shape. She looks for color, and shape. We spot more game than all of our other hunting friends combined.
BTW- she now owns her .44 Mag carbine, a Rem 7400 in 30-06, two 20ga over and under skeet guns, a Moss berg 12ga pump, An old Carcano Carbine she confiscated from a nephew, a Browning A-bolt in .243, a Savage 30-06, a Ruger Mini-30, and a Custom Mauser in .35 Whelen she confiscated from me. All have shortened stocks except the Carcano and ruger they were already short.