There are thousands of free books, both classics and new authors. If you keep a watch on the Amazon Kindle homepage, you will occasionally get a big-name author doing one of their books free for a short period.
The Wi-Fi Kindle is the one I have, and it works by connecting to your Wi-Fi network. If you find something you want during your lunch hour at work (for instance), the book will download to the Kindle as soon as you get home and turn the Kindle on.
The 3G version works on Amazon's own Whispernet which downloads the books direct to the Kindle. This is ideal if you don't have Wi-Fi at home, or if you are away from home.
Personally, I would never be in a situation where I didn't have enough books on my Kindle to keep me going long enough to get back home, hence I chose the Wi-Fi version.
I've had my Kindle since Feb, and have only 14 books that I've paid for (mainly for my mothers' Kindle as she has no internet and it was registered to my Amazon account), and yet in my Kindle archive, I have 197 books.
You can also download free books from other sites (not sure if you can mention them, but Smashwords is a good site). These you download to a folder on the computer, and then use the USB cable to transfer them to the Documents folder on the Kindle.
It's honestly pretty much foolproof
*Beware of "one-click-itis". It's incredibly easy to just click and download! Potentially injurious to financial health