Hello DesertGrandma and welcome to MobileRead. I signed up here in January just about the time I placed the order for my Kindle. It arrived in mid-February and I've been thrilled with it since. Not only can you purchase books from Amazon, but anything in Mobipocket format (well, those without DRM protection) can be read on your Kindle.
For classics, there are many (and I do mean
Many) books available for download (free, no less) here at MobileRead. You can jump straight to the book listings at
https://www.mobileread.com/forums/ebooks.php or click the "E-books" link in the blue menu bar under the logo.
Then, if you didn't find enough books to read, amble on over to Feedbooks (
http://www.feedbooks.com) and ManyBooks (
http://manybooks.net) and grab even more free books. If you're a fan of pulp fiction, one of the best sources is Munsey's at
http://www.blackmask.com/
Oh yes, I forgot to mention two sources of excellent science fiction. First, Baen offers many of their titles for free at
http://www.baen.com -- and you can buy even more Baen titles at WebScription eBooks (
http://www.webscription.net). Steve Jordan is an SF author who frequents these forums. He offers one of his titles for free at his website --
http://www.stevejordanbooks.com/ -- and an amazingly low-priced bundle of the rest of his novels.
From time to time, you'll find postings about special deals and free books to be found elsewhere. You'll want to keep hanging around here at MobileRead. Be sure to let us know how you like your Kindle when it gets there.