In short, don't buy a £300 console. Spend 2K and build a decent PC
Personally, I have a PS4 for 'pick up and play' stuff like GTA, Fifa(x) and a solid custom PC for the real gaming when I actually have more than 2 hours free time (rare) but as for the OP's question, yes there is some backwards compatibility on the Xbone and for your daughter im sure it will be more than good enough to fill the time between Homework/Going out/Work/Chores (delete as applicable)
Depending on what you/she plans on doing gaming wise then that should decide what you buy. Quick pick up and play PS4/Xbone, serious gaming and pretty much anything else then it's a PC you need. Horses for courses really.