Essay topics should take the following issue into account: the key question about Billy Budd has always been whether Billy's execution was necessary, as Capt. Vere believes, to maintain order and discipline on the Bellipotent. By the order of maritime law, Billy had to die for his crime of striking an officer--but the novel raises the question of whether it is always right to follow the law in every detail.
First, attend to the historical background. In the 1790s the British were at war with France, and mutinies frequently occurred. What bearing does this have on the nature and enforcement of maritime law at the time?
Second, you could address the question of the legality of "press ganging," or forcibly enlisting, sailors from other ships.
Lastly, you could examine the actions of Capt. Vere and the other officers who condemned Billy to death. The officers did not believe that Billy was guilty of the charges leveled against him by Claggart. In some sense, they must have known that Billy was in the right when he struck Claggart, and Claggart's death that resulted from this was an unfortunate accident.
The name of the ship Billy was taken from was Rights of Man, alluding to Thomas Paine's anti-monarchical book. So when Billy says, "Farewell, Rights of Man," his farewell takes on a double-meaning. Melville thus comments on the situation of men serving in the Navy. Early in the novel, Melville includes a chapter extolling Horatio Nelson, the admiral who helped lead the British to many naval victories and died in the Battle of Trafalgar. I would try to relate this to the novel's central theme and ask why, if Melville is questioning the rightness of maritime law, is he so intent on glorifying a traditional hero of the Navy?