Re: new or used??
A New Cheap Sax will end the joy of learning. I have seen and attempted to play and adjust a number of the less than 1000$ saxes. (I play and repair them) Their quality control tends to be pretty loose. A few of them may be OK, you might get lucky. Most of them are harder to play than a quality student model, as the pads do not seal consistantly, and next to impossible to keep adjusted even if you get a good one to start. You would be better off renting a quality student model to see if she will continue with it.