If you are getting it as a way of encouraging reading then don't get the Fire as it's more about films, games and music (with books as an added possibility). Of course, that is the one your daughter would probably want as it is the best "gadget" and more like an iPad than a eReader.
I would go for the £109 Kindle Paperwhite Wi-Fi as it has a touchscreen and built in light. If your budget stretches to the £169 3g version, then it means she can download books when away from your home wireless network (i.e. at school, on the bus, on holiday abroad). However, if she's organised, she can download hundreds of books at home and never need the 3g connection.
If you're on a tight budget, the £69 one is simple, but very effective (no light built in, no touchscreen, no 3g roaming connection)