Revenge is the main theme in Hamlet. There are many ways to look at revenge in this play. I would think the fact that Hamlet is grappling with his task of avenging his father, the king's, murder is a good way to go. The ghost implores Hamlet to seek revenge for his untimely death. Yet, in this play, revenge is not carried out rapidly. Hamlet contemplates his task and does not act until the end, and it results in his death, as well.
The theme of death is great to explore, as well. The murder of the king is the first in this play, but certainly not the last. There are many characters whose deaths are intentional rather than natural. Hamlet, his father, Claudius, Ophelia, Laertes, Polonius, and Gertrude all died in this play. (With the exception of the king, that has already happened when the play opens). You could explore the causes and impact of each of their deaths, and relate it to Hamlet's demise.