"To be, or not to be" is the main issue as Hamlet searches for the existential meaning of his life. Faced with
- the weakness of his mother and her disloyalty
- the hypocrisy of Polonius,
- the treachery of Rosencrantz and Guildenstern,
- the ambivalence and vulnerability of his love, Ophelia
Hamlet wrestles with his faith in life and his disgust for the corruption of the Danish court. However, Hamlet, who has declared himself "Hamlet the Dane" after seeing Ophelia buried, determines to act nobly after witnessing the kingly behavior in Fortinbras who risks his life "for an eggshell" and rid Denmark of its corrupt court.
You are lucky that this play is loaded with issues! Here is a quick list of things that you could then investigate further and possibly create an argument about:
1. Is the ghost a real ghost of Hamlet's dead father, or is it just a devil in the disguise of King Hamlet who is trying to damn Hamlet's soul?
2. Does Hamlet truly love Ophelia?
3. Is Polonius a mean, calculating politician, or a self-involved fool, or some mix of all of that?
4. Is Hamlet appropriately sorry for killing Polonius?
5. Why did Ophelia go crazy?
6. What does it say about Hamlet's character that he is familiar with the Players and the theatre?
7. How good a friend is Horatio? Rosencrantz and Guildenstern?
8. Why is Fortinbras in the play? Why is Hamlet motivated by Fortinbras's actions?
9. What is the relationship between Gertrude and Hamlet?
10. Why is Hamlet different in Act 5 -- more willing to take action?
11. Why is Hamlet always talking about death?
12. What is the purpose of any of the scenes of comic relief in the play?
13. Why does Hamlet "set his election lights on Fortinbras" at the end of the play?
14. What purpose is served by Rosencrantz and Guildenstern's deaths?
15. What is ironic about any or all of the deaths in the play?
16. Why does Laertes respond in such a dramatically different way than Hamlet does to the death of a father -- Laertes willing to damn his soul for revenge, while Hamlet will not?
17. Why can't Claudius receive God's forgivness for his crimes?
18. Why doesn't Hamlet act sooner and with more outward vengeance?
I hope this is the kind of thing you were looking for!