This question could be answered in a number of ways. One approach you might want to consider is looking at how each main character struggles with conforming to a sense of outward expectations versus listening to what seems right inwardly. To do this, consider the character's personality traits and compare them to his actions throughout the story. Does he act on his conscience or on a sense of outward expectation? What is the ultimate result of his actions?
One of the more obvious examples is the character of Captain Vere. Vere is described as a man of natural intelligence, a keen sense of duty, and fair yet high expectations. As a result, he is well respected, maintains a sense of order on his ship, and is trusted in decision making.
When the beloved "handsome sailor," Billy Budd, strikes out in anger against John Claggart and kills him, Vere is, for perhaps the first time, faced with a morally difficult decision. He must decide between convicting Billy of murder and perceived plans of mutiny, or going with his gut belief that Billy is truly innocent.
In the end, Billy is convicted and hung, due in large part, to Vere's convincing the court not to let their love of Billy affect their view of the factual events of the incident. The events after the hanging are briefly described, but basically, we know that the crew erects a monument to Billy Budd, Captain Vere dies shortly afterward in a battle with a French ship, and the remaining men each take pieces of the monument and hold them up in a gesture of honor to Billy Budd.
As one of Melville's less significant works, Billy Budd is perhaps one of his most highly debated stories. At the end of the novel, the reader is very clearly presented with the question: Did Captain Vere make the correct decision? (Or, was justice truly served?) This question has been considered by many to be the central idea of the story and the fact that it is left ambiguous allows each reader to come to a personal conclusion. I encourage you to look at the other main characters in the same way as above and draw this conclusion for yourself. Good luck.