You could obviously have several possible approaches to this prompt, but I think that meeting both Claudius and Hamlet in scene 2 makes it logical to focus on them. Even though Hamlet is the protagonist of the play, I think a reaction to Claudius is actually more interesting at this point in the play.
Claudius opens the scene with a long monologue to the court and in it I get the sense that he is trying to be appropriately behaved for a new king who has come to the throne and his new marriage in a kind of unseemly way. He only has the throne because his brother the king has died, and he is only married because he married his brother's widow. He says all the right things under the circumstances, but it is all still a bit off-putting -- especially when he says thank you for "going with this affair along" almost acknowledging the inappropriate nature of the situation.
He then goes on to be very dismissive of the external threat that young Fortinbras is posing and reports that he is sending a letter to the man's uncle in the hopes that he can reign him in. His final words, "so much for him" seem overly confident and a bit arrogant. I can guess that he wants to send the message to the court that he is not intimidated and that he has control of the situation, but I still don't take it that way.
As the scene continues, we see his attempts to act fatherly to his nephew, now step-son. He really should know better than to think that a grown man like Hamlet would want to be called son by a man is completely NOT his father and has always been his uncle. It seems to be rubbing it all in Hamlet's face a little bit. He then goes on and on about how Hamlet should be getting over the mourning of his father, saying that the grief is "unmanly" and a sign of "stubbornness" and "a fault to heaven." He hits on all the possible weaknesses in Hamlet in an effort to get him to let it go when really he just doesn't like how the behavior looks. After all, if young Hamlet is in deep mourning, then maybe Gertrude and Claudius should be too -- instead they are newly married!
Claudius comes accross as insincere and arrogant in this first meeting, and it sets tone for the later scene in which the ghost of King Hamlet returns from the dead to reveal the whole truth about Claudius's murder of him in the garden. Hamlet says, "Oh, my most phophetic soul" not because he suspected Claudius of murder, but because he knew Claudius was that kind of man.