I think another interesting thing to look at is Claudiusas master manipulator. Look at how he handles Rosencrantz and Guildenstern, Polonius and ultimately Laertes to do his dirty work in regards to dealing with the threat of Hamlet, first when he is "crazy" and later, once Hamlet reveals that he knows the whole story of the murder.
I think a good thing to argue would be something like this. "The murder of Hamlet was more political motivation than passion." Claudius tells us of the three things which guided him. "Of those effects for which I did murder--/My crown, my own ambition, and my queen." Despite a popular belief, Hamlet is the only person to create a passionate relationship between Claudius and his mother. By Claudius's own admission, Gertrude was a distant third.
I would think a good thesis statement would depend on what you wish to prove about Claudius.
Perhaps a good place to start would be the idea of power and what men, in this case Claudius, do to get power and retain that power.
Ask yourself questions about the character. Does Claudius love Gertrude or is she just a means to an end? Is he a good king? Was Hamlet's father a good king? Why is Claudius king and not Hamlet who is the prince? What lengths does Claudius go to neutralize Hamlet? Is Claudius a smooth talker, able to manipulate people?
The answers to the questions above and others will help you discover what you wish to prove about Claudius. The result should be a strong and provable statement.