You have to make sure the laptop you buy meets the requirements to run Vista (Windows new operating system that will be released next year-->laptop prices are quite low now because everybody is holding out till Vista is out)
It's important to know how much she will have to carry it around as it makes a huge difference in the size and capacity of your laptop - If your daughter wants to use it for graphism in a nearly professionnal way it won't be with the little thing she'd like to carry around -
The CNET buying guide should help you see what's needed
http://reviews.cnet.com/4520-7602_7-...1.html?tag=dir
Also if she is 16 she should be quite interested by the look of the machine, so you could maybe pre-select a few ones with the specs you need in your price range and then ask her what she prefers (unless it's a surprise...I've got a feeling my dad is gonna give me a new laptop for my birthday tomorrow as well