You don't need to buy only from Amazon. Side load any content from your computer using the USB cable supplied. I have audio-books as well as music in my Music File (mp3 & mp4) organised in playlists. All work fine. You can't only store them on Amazon's cloud. Either keep them on your device or use one of the other free cloud stores like MS Skydrive and temporarily download them.
I've also downloaded non-Amazon content direct to my Fire HD. I keep a lot of books and podcasts - again mainly MP3/MP4 often the app makes a new internal folder. Move them into Music or use them through an App. ES File Explorer App (free I think) is a great help but you can also use Explorer in Windows which shows up your device as an external drive when connected through USB. This helps you move things around on your device.
Hope that helps. Graham