iPod touch is phone sized, uses the Apple store, kids seem to use it easily.
Kindle fire doesn't have access to Android apps, so very limited for apps by all account. Is 7" in size, is classed as an e-reader, so very good for books, has access to Amazon, but has tablet stuff on too, so internet, etc. On offer for £99 at the minute.
Another option is the Nook. Is also an ereader, but has access to the Android Play market, so lots more apps available. Can get the Amazon app to order books from Amazon, or from the Nooks own website (Barnes and Noble). 7" screen is currently £79.
We currently have an iPod touch in the house, is very handy for car journeys, etc, and playng on apps, but no good for reading. I'm currently looking between the Nook and Kindle Fire for Christmas for DD (9.5) and I'm leaning towards the Nook personally. DD has had her iPod touch for almost 2 years, still going strong, although rather scratched now!