Didn't Weston say-----"composition is the most important part of seeing", or something like that....
The OP inquires about those things that are important about "producing" a photographic image, it seems to be inferred that he means a successful one too, then, perhaps not in any specific order, but what pass for me to be a successful photograph:
1. Composition as it relates to the subject (this has to be there somewhere)
2. always maintaining the impression or sense of light in the image
3. the presentation of the gray scale in the photograph as I visualised it
If I can get those three things to come together on the surface of the print, I'm pretty pleased with it, even if it is not too impressive to anyone else.