OK, I'm no expert in this stuff, but:
Post-modernist: The "unemployment" picture is just as validly reinterpreted as a beautiful scenic view of a river symbolizing X to a particular viewer and Y to another viewer and all interpretations are equally valid even though the author had interpretation Z in mind when it was created.
New Criticism: The structure, composition, and choice of subject matter all lead to a particular interpretation/meaning, and this meaning is that of the author who crafted it in such a manner that its meaning could be seen by the viewers. Sometimes you have to dig into the life of the author (maybe) to figure this out, but the meaning should stand on its own apart from the life of the author or comments the author has made, those facts only strengthening the value of the work.
Historical/Traditional: In order to understand the photograph you have to study every aspect of the author's life and the circumstances surrounding the creation of the photo, including whatever the author said about it and anything else the author ever said or did. Who did they borrow from? What are their influences. And their shoe size. Shoe size is very important. You must start with this study and then, only after digesting it all, go look at the actual work of art to be able to understand it.
Societal: What does the photograph say about the people who are in it (or who live in the place where it was taken)? How is the author reflecting/strengthening/challenging the society in which he/she lived and took part in? What did it cost for a photographer to live and photograph in Pittsburgh? What types of audiences was he/she trying to reach.
Gender: The sexual orientation/gender of the photographer is a characteristic that imbues meaning into all of their work. Consequently, rivers mean women, factory smokestacks mean penises, etc., etc. (I know I'm trivializing, but this sort of work is so abused it needs some trivialization. Not that it sometimes isn't valid, but every upward rising cadence in Tschaichovsky doesn't necessarily figuratively symbolize an ejaculation, if you know what I mean.)
I'm sure there are others...
While I'm willing to accept post-modernist criticism on its surface I find new criticism (which I think was invented at Yale in the 50s so I'm not sure why it is "new") more insightful and thought-provoking. Especially when it is coupled with some historical study of the author, especially that surrounding the creation of the work itself, and some historical understanding of the societal underpinnings. And I think New Criticism will draw on any method of interpretation as long as that method can be supported by something in the work itself. The craftmanship of the author is just as important as the societal influences, the sexual influences, and the historical influences.
As far as talking about your own pictures, to quote Louis Armstrong "if you don't get it, man, you ain't never gonna get it."
Will