Whatever rifle fits her best, chambered in .243 Winchester. Look at the youth models if she's smaller in stature, as they'll probably fit her better and be lighter. Fit is important for perceived recoil, and while the .243 is quite light, it could still start to hurt after several shots if the rifle fits her poorly.

I'd take her to the store with you and guide her through holding several rifles in your price range and then let her choose.

Mike