I agree with starting off with a half lease! If your daughter finds she enjoys regularly riding 3 days per week and wants to spend even more time at the barn then look for a horse to purchase.
Someone alluded in a post above to being cautious about getting a horse that your daughter cannot grow in to. She may not see herself as a competitive rider now, but with more hours of riding she might find that she is really keen on it and you don't want her to quickly outgrown a horse within a year! She should try a munch of types of horses before deciding on which she likes and doesn't like. (Two people have told me when I asked them for advice on buying a horse, first thing: you have to LIKE the horse when you're standing on the ground as much as when you're riding)
I leased for a year and being able to ride the same horse 3 days per week, without all the potential medical worries, was a wonderful, educational experience for me.
Very exciting opportunity for both you and your daughter! Wishing you luck with which ever route you decide to go!