Here's another warm AGF Welcome, deerhoundmom. Glad to have you join us!
Yesterday, I played a Takamine that was pretty similar to the EG333C. It played well, had decent and volume, and was a lot of guitar for the money. Yes, there are other good choices, but I don't think you will go far wrong in getting her this guitar. Coming from you, I know she'll enjoy it even more.
If she has access to the internet, there are tons of free guitar lessons on Youtube, some of which are pretty good. Personally, I prefer having a real teacher, one who can provide feedback and motivation and can adjust the lessons to the needs of the student. If your daughter's teacher is too technical for her needs, I'd suggest that she tell him/her that. A good teacher knows how to teach what the student wants to learn.
Good luck! Hope you'll stick around and enjoy the conversation, even after this guitar has found its new home.
cotten