So one year old is pretty much ancient in tablet years, but there are still some perfectly good sales on last year's model. I had several relatives ask me about it while I was eating my Thanksgiving dinner, so I thought you might like a bit of a guide on the subject.
Yes, that used Kindle Fire is perfectly functional, though it has the same caveats I gave you last year. The Kindle only shops on Amazon. If you're happy with that part, go for it. Otherwise, you can get an Android tablet that lets you download both Nook and Kindle books.