Yes, you are going to have to decide if you want just the ability to read books or if the music/audio books is a must. My DS has a Kindle paperwhite and I keep it filled with library books. Amazon has great tutorials about setting it up for children. There is an "experimental internet" that I have disabled. He also has an iPad with the Kindle app so he can read on that. But we do not allow him to have the iPad in his room or take it outside the house but we allow him to take the Kindle anywhere.
The Kindle Fire is a full-fledged tablet with apps much like an iPad. It will do everything you want but will also come with internet access and the ability to download apps and games. There are parental controls but I'm not sure what you would be able to disable.
You could consider a basic Kindle then a basic MP3 player for music and audio books. The MP3 would need to connect to a computer to download music and audio books.