I bought a Kindle touch (not the latest touch version) for my wife. She was somewhat hesitant, but liked the eInk approach and has read some things on it, but she's old school and still prefers hard copy books.

I don't believe that Nook can read Kindle books nor vice versa. Kindle books are .mobi formatted files, Nook uses the more generic ePub format.

I suspect that most if not all tablets out there today can read either format via free apps. So if you have an Android tablet (I do), you can download from the Google Play store either (or both) of the Kindle reader and Nook reader software applications. For free. From there you can purchase books for the respective application (i.e., from Amazon for Kindle, from B&N for Nook) via the application, or via website using a web browser. You can also side-load apps to either one, i.e., get a freely available book in .mobi or .epub format, plug your tablet into your computer, then copy the file over to the appropriate folder on your tablet. Then when you next start the reader app the book appears. Of course there are a lot of free classic (out of copyright) books that you can download directly from B&N or Amazon.
And lots of stuff via places like gutenberg.org, baen.com/library, etc.

Kindle Fire: I have no direct experience but it's basically a decent Android tablet that has the user interface sort of intentionally crippled a bit to make it focused on buying things from Amazon. There are ways to mitigate this to use it as a more general purpose tablet, but you would have to search for details. Just look at the specs for the specific Kindle Fire model you're looking at --- I don't recall if the newest one has a camera built in? You can certainly transfer photos somehow; if you can manage to open it up to generally adding Android apps from the google store (and Amazon has quite an android store of its own) you can find something to wireless connect to transfer apps I would think (I can on my android tablet). But more typically I plug it in to my computer to transfer files.

A blog I subscribe to talks about getting a new 8.9" Kindle Fire HD for $50 off today, a wi-fi only model. You order this model: http://www.amazon.com/Kindle-Fire-HD-9-inch/dp/B008GFRE5A and enter FIREHD89 as a promotional code at checkout to save $50. I have no idea if this is a good deal or not, but based on what I paid for my 10" tablet, I suspect that it is --- assuming this product really is right for you.

I don't mind reading on an LCD screen at all, but for other people it's got to be the eInk display. The Fire models are all LCDs I believe.

This stuff is complicated; best of luck figuring out just what you want!