How do I write a research paper on The Red Convertible?
You're in the right place, but we can't answer in that much detail here in the discussion forum. You definitely need to use the enotes study guide for this. It's an excellent resource for all of this information. For example, you can read summaries and analysis, but you can also access criticism, author background and other information about the story.
I have identified the areas I think you'll find most useful.
Essays and Criticism: Complex Symbolism
The major outline of your paper could logically follow the path your question details: reasons author wrote; historical background (events around the time of writing); author's attributes; contemporaneous audience reaction (possibly also present day audience reaction); universal value that will render the work applicable to future audiences (enable it to resonate with future audiences). So to start working on your paper, since you now have an outline, you might start at the top, "reasons author wrote," and work your way through. Although it is perfectly well and good to start on any section of the outline, if you prefer, then assemble the sections according to the outline--with appropriate transitions--when you have all researched and drafted.