Okay, here's some basic choices:
A) Do you want a back-lit LCD screen or an e-ink screen?
E-ink is much easier on the eyes, requires less battery, looks like the page of a regular book. These are the e-readers that are designed to be read for many hours like a physical book. I have an e-ink Nook because I wanted to read on it, and add my own documents (lots of scholarly papers in pdf, etc when I was in grad school). The basic Kindle is also e-ink, Google also has one, and there's some other good ones out there too, the only one I wouldn't recommend is the Kobo since that's the Borders one for obvious reasons.
You can check e-mail/use the browser, but its difficult and slow most of the time, and the games are pretty much just chess and sudoku on most models.
The e-inks usually run around $100.
LCD screens are like your computer, and this is what the Kindle Fire/Nook Color/iPad, etc will be. These "e-readers" function more like tablet computers than reading devices, but are much slimmer and more convenient than your laptop/netbook might be. Lots of games, lots of versatile functionality, can watch movies on them, etc, etc.
These usually run around $250+.
So, what do you want to use it for? That will determine which kind you start with, then go from there as to which has the best features for you ... do you want open source (ability to put your own content on?) or ease in buying content, etc ... lots of apps?
Top Ten Reviews also has a nice summary of compare and contrast features.