Yes, putting your downloaded books in the "documents" folder is how it's supposed to work. In order to organize them on the Kindle, you'll need to set up Collections from within the Kindle itself. There's also some sort of
Windows app for doing it on your computer, written by one of our very own MR members.
While putting your books into subfolders doesn't do anything to sort them on the Kindle itself, it can serve a useful purpose. I split up my books into various subfolders for library books, favourite books I want to keep and have with me at all times, books I actually went and bought, free books I'm just trying out, etc.
This way I can easily back up any new samples/purchases from Amazon (gets downloaded into the top-level of the documents folder, after which I move them) as well as the .mbp files for the notes and highlights from my non-Amazon books. It also makes it easier to delete stuff I'm no longer reading/just couldn't finish.
Hope this helps, and welcome to MobileRead, both of you!