Is there any one character whose actions illustrate the theme of appearance and reality more than others? Explain.
I'm guessing you mean "appearance vs. reality"—a prevalent theme in many literary texts.
In Hamlet, Claudius represents this theme, as does Hamlet. Claudius appears to be the mournful brother, lusty husband, and loving uncle; yet, he committed both regicide and fratricide in order to fulfill both his desire for power and probably his desire for Gertrude as well. Almost everything he says has a double meaning. While he pretends to care for his nephew, he actually sees him as a threat to his power and then a threat to his safety—so he plans to murder him.
Hamlet chooses to "disguise" himself and his motives in order to discover the truth. His "madness" (confused by Polonius as a result of Ophelia's rejection of Hamlet's love) has nothing to do with Ophelia and everything to do with uncovering the truth of his father's murder.