...except the sending to my Kindle part. I would find the book in the Manage Your Kindle area of my Amazon account, and it was very easy to choose "which" Kindle device to send it to, but the books didn't appear on the chosen devices until I opened the Kindle software on the device, found it in the Amazon archives for my Kindle account and selected and downloaded it from the actual device.
So I think you can skip the part about going to the Manage Your Kindle area and sending it to the Kindle you want. Just do that part from the Kindle itself.
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If the Internet is as good as I hope it will be on the newest Kindle fire, you should be able to visit your library, check out and return books, all from the same device. After having (and loving) my iPad this year, I am looking forward to being able to (at a reasonable price) actually compare it with the new Kindle tablet (android) back to back. It will be fun!