None of the Kindles have back lighting. The DX and both K3's have the same Pearl EInk screen as the newer Sony's.
If the one you saw was about the size of a piece of notebook paper, it was DX. If it was smaller (like the size of the Sony 650, I think) it has the 6" screen.
When you buy a Kindle, you can set an email address in your Amazon Kindle account to send documents to your Kindle. It would be something like your
username@kindle.com but if you live in the US you can also send the same documents to your
username@free.kindle.com and you won't be charged. Although most people don't get charged no matter which one you use. I've never been charged anything but I don't use it as much as it sounds like you will.
Sending it that way is only to convert it to kindle format. But you can convert them in Calibre and then sideload documents free. Also I believe that as long as you send them to your Kindle email address and use a free WIFI network when you do it, it will be free.
The charge only applies sometimes when you are using 3G to do it.
The newer Kindles now have better support for PDF's so you may not have to convert them at all. You can also switch the screen to landscape and also zoom in.
I don't know how this compares to a Sony because I don't own one.