Here is an awesome way to get free books on your Kindle:
Do you know about Project Gutenberg? In case you don't, it is a free, online library of books that are out of copyright. There is a huge selection of what most folks would call "classics." Unfortunately for you, it is mostly fiction, but there is some old non-fiction (think Darwin and other 19th-century stuff).
Project Gutenberg is a library of free eBooks.
www.gutenberg.org
Anyways, your kindle either already has an email address or you can set one up through your amazon account. It is totally free. Use a laptop to search through Gutenberg for books you might be interested in. Download the files for the books you want. Then, email them to your kindle email and "sync" your kindle with your amazon account. The books should pop-up, ready to read.
As far as book recommendations are concerned, I'll add two fiction and one non-fiction (there are already many great recs here):
Moby-**** (on Gutenberg)
Moby **** is not as intimidating as you might think. I fully expected to be bogged down by a, well, whale of a book. That was not the case. Moby **** is actually quite approachable, and believe it or not, humerous at many points. I would argue at length that this is THE great American novel, and as such, should be read by anyone that wants to understand what America is. Better yet, it is a hunting story. I think about this book every single day.
Butcher's Crossing by John Williams
This is a story about a young man who drops out of college to go see the west (and the buffalo) before it disappears. He hires an outfit to go hunt buffalo and...things don't turn out the way that they are planned. If you liked Rinella's American Buffalo, I have a feeling you'd like Butcher's Crossing, too. Everyone that I have recommended this book to has loved it. Also, you better watch it before the movie comes out. Nicholas Cage is going to torpedo this awesome story into another National Turd
Alaska's Wolf Man, the 1915-1955 wilderness adventures of Frank Glaser
It has been awhile since I read this book, but I remember not being able to put it down. Frank Glaser trapped and shot wolves for the US government when they were using caribou in place of beef. Awesome book, though I never see it recommended. I heard about it from a guy who lived in AK for a summer.