I'd let her shoulder rifles and see which one she likes the best, then pick an appropriate caliber in that rifle. If you pick the caliber first you'll limit your options. I feel qualified to comment on this thread because I've shopped a lot of youth models (I prefer a shorter LOP).
I liked the fllowing (in this order)
Weatherby Vangaurd S2 youth. Excellent trigger, light, compact, acccurate, and Weatherby stands behind their products. This is what I bought (mine is in 308).
Browning x-bolt micro midas. Wonderful fit and finish, fine trigger, great looks (I didn't like the stock).
T/C dimension/Venture compact. Very functional, OK trigger.
The Ruger American is something I'd avoid, as are the other super budget rifles. I'm sure they'll kill deer fine, but why bother with a so-so trigger and poor fit and finish unless you absolutely don't want to spend the money.
Savage makes a lady hunter that looks nice, but I've never shouldered it. All of them will be chambered in 243 and 308. If she plans to shoot a lot I'd probably choose one of those two calibers. They are most plentiful, have the most variety of ammo options, and there are some cheap plinking ammo options (especially for the 308).