My opinion stay with the .308.........
Remember..She is going to be practicing lots with this gun,and a sore shoulder will happen that may result in flinching.....
The .308 is very inheritally accurate cartridge and these helps when shooting long ranges as well even in cheaper designed guns.....

But if your thinking of the .300WSMyou got to think of the gun your buyng the caliber.in.
I don't know what the recoil will be like in a .300WSM people are already mentioning adding recoil padding..
Not to mention the creep,over travel just in your trigger pull.
I think it wouldn't be very pleasant cal to shoot in a cheaply priced and built rifle and it certainly won't shoot as accurate as others on the market.
Terminal ballistics don't mean a thing if you can't hit the target........
Amuch better choice would be the Savage/Rem/Weatherby in a higher grade/models thiswill help reduce the recoil cause the stocks will be better suited to handle the recoil and the barrels will be made of better steel.Overall you get a finer tuned in gun that will be alot more pleasant to shoot..

I wouldn't settle if all you can afford is a Stevens, maybe look for something alot better second hand...
They are out there..