Mark,
I teach Hunter safety and I'm an NRA Shotgun Instructor. I went through the the same thing with my daughter. One thing that makes my skin crawl is watching adults making kids try to use a shotgun that does not fit, they can't easily operate or is so lite the recoil makes them gun shy. 20 ga is a good choice for starters, that is what I would recommend.
The approach I used with my girl cub was to determine her eye dominace (wether right or left hand action is required), then what type of action she was the most comfortable with, (we tried single, side by side, over under, semi and pump). She liked the over under so I bought an inexpensive O/U and cut the stock down to fit her, she is starting to break clays and has gotten a few rabbits and squirrels. And her confidence really took off.
Semi-auto helps take away the recoil, singleshots like the NEF youth (20 ga) rattles my teeth. Rumor is the portion of PA I live in is going slug so we are doing the same thing all over again but with slug guns and her preference this time is a pump.
All of the maunfacturers make youth models, find the one in your budget and is not intimidating to the new shooter, if they have the right tool, it's easier to get them hooked for life. That is my opinion and I hope I did not muddy the waters more for you.
Ga65
God Bless the Troops and their Families.