Montag is a "company man". He basically follows the company mantra and follows the rules of society. Montag is frustrated, but he is also aware that he is being watched and monitored for "abnormal" activities. The mechanical hound detects changes in Montag's chemical make-up and acts aggressively toward Montag. Montag represents the oppressed worker. He is being crushed by the system, and there is very little he can do about it except rebel.
Montag eventually comes to grips with an oppressive regime that has in many ways betrayed its citizens by keeping them from knowledge contained in books. His only solution appears to be a negative one until the very end of the book. Bradbury's novel exemplifies how an oppressive regime can create rebellion from the citizens within that regime.
Clarisse is a "free-spirit". She simply does not accept the rules or order of the society in which she lives. Clarisse questions everything which is in direct opposition to the idea of censorship. She appears to have insatiable curiosity and a desire to experience things and know the "why" behind many of the societal rules. I think Clarisse exemplifies childhood innocence and curiosity to the reader.
Clarisse in many ways is an opposite of Millie, Montag's wife. She is not really rebellious because she has never really accepted the rules of the society. Millie, on the other hand is totally accepting of the society and rules in which she lives, even though it is unhealthy and costs her very nearly her life.
I will say that Clarisse is handled much better in the film (1966) version of this book than in the book itself.