1) What's the difference between a Kindle and a Kindle Fire? Is one a dedicated e-book reader, and the other a sort of mutant Android tablet?
2) Do most people these days by Kindles, or Fires?
3) I'm looking at Kindles on the Amazon site -- what is an "ad supported" Kindle?
1) A "Kindle" is only for reading. It has an e-ink screen, which uses magnetic particles to display the print. It has no glare, and is very similar to reading a paper book. It is not like a computer screen. A "kindle fire" is just another computer tablet, like an i-pad, with a flat computer touch screen display. You can read books with them of course (including those in kindle e-reader format), but it is harder on the eyes than the e-ink of a kindle reader.
2) I don't know. Ebooks can be read on either though.
3) Ad supported kindles are cheaper versions of the kindle, but they display banner ads at the bottom of the menu, and they also have an ad on the "sleep" wallpaper. So you save some money by agreeing to have these ads. You can pay a sum to amazon after the fact to have the ads removed if you change your mind.
Kindle readers are wonderful for those who like to read a lot. I have hundreds of books on mine, most of which are free public domain books (project gutenberg, or amazon). My local library has an e-book loan program also. With amazon, you can get samples of their books sent to your kindle as a preview to see if you want to buy the book. Click a button, connect to wireless and your sample is loaded automatically. Or if you buy a book, it arrives instantly.
Another benefit to kindles is that you can hold the book and turn pages with one hand. This allows me easily do things like walk a track while reading, or you can eat with one hand and read using the other and so on. Perfect for book lovers.