I got my first horse at 14 and loved it, I still have him now 18 years on!
First things, you'll probably need to learn how to look after a horse. My parents had to help me a lot. Personally I'd steer clear of a riding school set up as they'll want the horse when your daughter will want it most.
As you aren't horsey the best set up would be to have the horse on full livery (cared for 7 days a week) approx £120-150 per week or possibly part livery where you do the weekends, but this will mean 2x a day and no lie ins ever! This way the yard owner will have a lot more input into the care of your horse and will be able to advise on feeding and help when the horse gets injured (I say when because with horses this is an inevitability!)
You've got a good budget for a horse, but the key thing will be to get a good natured horse that doesn't over face your daughter. Often the flashy looking ones, whilst pretty, require constant work and can easily become unmanageable if not looked after properly. Ideally I'd buy something over 7 years old so it's got a bit of experience behind it. Be very careful buying from dealers in that area, there are a number around there who are very dodgy.
Ideally you should take an experienced person with you to check the horses temperament and conformation. A bad conformation can cause lots of problems down the line. Without doubt you must get the horse vetted, by your own vet (don't use theirs) and bloods checked prior to purchase.
You may do well to start a thread on the horse and hound forum, there will be lots of people there who will be able to help.