The first thing you really need to determine is what kind of money do you want to spend. You can buy a laptop for $300, but it won't be worth anything by the time she is a freshman in high school. Not only will it not be worth anything, half the programs she will need or load onto it for school will crash the system because it's not powerful enough. A good piece of advice is buy something that will last her long term, say all the way through high school. Granted her senior year the laptop might be a dinosaur, but it will still allow her to type reports, research on the internet, check email and etc. I would highly recommend spending something in the $750-1k range with a computer that has some quality parts. The system you buy now might be a little more than she will need, but will last until she graduates high school.
So what kind of system should I buy? Well excellent question. There are a lot of brands out there to choose from. It's hard to go wrong with a Dell. If your worried about dollars, check out the Dell outlet section on their website. A lot of these laptops are brand new, even though they may say they are refurbished and in the outlet. What happens is people will order a laptop, cancel it the last minute, refuse shipment, send it back, or whatever and Dell will resell it. So they say its not "new" when it really isn't. So they sell it in the outlet area. Many times you can save 20-30% off on these laptops. If I get some time later this evening, I'll check it out and see if I can find a laptop that would be good for your daughter and post the specs. That way you can have a general idea what it is and what you can look for when shopping and comparing other brands/models.