You might want to think about the various themes in this excellent novel and use one of them to base your essay around. To me, one of the most obvious things to focus on would be the theme of innocence, and how Billy Budd is naively innocent, which of course becomes his tragic flaw.
One topic you might consider is the conflict between the rights fo the nation and the rights of the individual.
Does Billy Budd have a tragic flaw? If so, what it is? How is the work like a Greek tragedy?
You might also explore Melville's idea of the "noble savage" in relation to Billy.
There are other suggested topic ideas included in the enotes pages regarding this work. Check out the links below for more help.
A good place to start would be the “Billy Budd” area in our study guides. Use this link: http://www.enotes.com/billy-budd/themes or you can just do a search for “Billy Budd” and you’ll go to area with study guides, analysis, summaries, and other useful information on “Billy Budd.”
The some themes that could be explored in a long paper would be: Duty and Conscience; Innocence; Law and Nature; and Evil. If you go to our “Suggested Essay Topics” at http://www.enotes.com/billy-budd/suggested-essay-topics you’ll see many more possible ones that you could turn into a longer paper.
I also selected "Billy Budd" for my term paper in college, two years in a row, in fact, for two literature classes taught by the same professor. I wrote about the much debated question of whether "Billy Budd" was a homosexual character, and how that affects the overall purpose of the story. I took one stance in the first paper (assuming he was not intended to be homosexual) and in the next paper I took that side that he was. There have been plenty of published speculations on this very topic, and I personally liked that it was a subject that was outside of a traditional term paper focus.