Disagree that the keyboard one is necessarily better. My friend has a keyboard one; I have a Kindle 4? Her DH now wants a Kindle. She told him to get a Kindle 4 so she can have it and give him the keyboard one. Reason is that keyboard is heavier and doesn't fit in a handbag so easily.
I got mine for Christmas. I absolutely love it. I really didn't think I would use it as much as I have done. I have gone through the free books, signed up to eReaderiQ to get the daily e-mails about free books. There are usually some teenage books on there. If I were you, though, I'd supervise the downloading of books, or only do that yourself.
Tesco online are doing the Kindle for for £79! atm.
I have a leather cover for mine. Didn't really want one, but DH insisted and I'm glad that he did. It makes the Kindle easier to hold and to chuck into a bag without the screen getting damaged.
There are loads of classic free books on Amazon, too, such as Dracula, What Katy Did..., Pride and Prejudice, lots of Dickens.
I hope your DD loves her Kindle as much as I love mine.