I agree with either a Brother or a Janome for a first machine. I have 2 machines I use for myself ( An old White and a Janome) and my own DD has a basic Brother. None of my machines are computerized and I like it that way. I think it is a matter of preference if you get her a computerized one or not. How is she with computers, etc.? Do your research but I think getting her a sewing machine is definitely the way to go.
A little off topic, but have you thought about showing her how to hand sew? Good luck!