Hamlet...Crazy, Devious, or Both?

I have to admit, I enjoyed today's discussion on the character of Hamlet.  I really had never thought about the language that he uses and how he uses it to manipulate others.  I found the idea that "to be or not to be" could have all been for Ophelia's benefit an intriguing idea, as  in all the years of picturing Hamlet I had always envisioned him alone desperately grappling with the purpose of life, rather than putting on a facade for his family and friends.  We already know that Hamlet trusts next to nobody (with the exception of Horatio), as he plays Polonius for a fool, acts crazy around Ophelia, and refers to his childhood friends Rosencrantz and Guildenstern as "adders fang'd" (to say nothing of what he thinks of Claudius and Gertrude).  Is Hamlet aware that people are after him because of natural suspicion, or is he making things up and happening to be right? 
The fact that Gertrude cannot see the ghost in Act 3, Scene 4 would seem to me to lend a lot of credence to the idea that Hamlet is simply going mad.  Hamlet seems to have transformed the ghost into an aspect of himself, from a messenger showing the facts about the his father's death to a fiend driving him towards revenge.  As we discussed in class, Hamlet's casual murder of Polonius also demonstrates his erratic personality-Hamlet can't kill a murderer simply because he has encountered him while he is praying, but he can strike down an unarmed man just for listening to him behind a curtain (I see serious issues here with Hamlet's beliefs about revenge and how it should be carried out).  Personally, I am looking forward to discussing the play more in class.  Today's thoughts gave me a lot of insight about the play, and about how to analyze and look at the text, the context, and the characters.  Who knows?  By the end of our Hamlet discussion, I might have changed my mind on my verdict of Hamlet's madness.  Or I might not.  It all depends on whether I can learn to read Shakespeare in a different way than I have before.