When he is alone, or with Horatioand free from the need to act the lunatic, Hamlet is incredibly lucid and self-aware, perhaps a bit manic but hardly insane. The questions about death, suicide, and what comes after are left unanswered.
Her choice of songs seems to reveal two obsessions.
If you're murdered, then will you go to heaven? Bradley has pointed out, in his very first long speech of the play, "Oh that this too solid flesh," Hamlet seems on the verge of total despair, kept from suicide by the simple fact of spiritual awe.
Polonius' grasp of language, like his political instinct, is quite shallow -- he gestures toward the mastery of rhetoric that seems like a statesman's primary craft, but he is too distracted by surfaces to achieve any real depth.
Hamlet thinks deeply about it, and perhaps "contemplates" it in the more popular sense; Ophelia perhaps commits it. As a mere student of advanced-level English Literature, I doubt I can add anything new to the debate in words, but I can look at the evidence supporting or dispelling each argument and come to my own conclusion.
Ophelia's breakdown and Hamlet's "north-north-west" brand of insanity argue for Hamlet having a method to his seeming insanity From the way the characters talk, we know Hamlet has been wooing Ophelia for some time.
When Hamlet uses the proverbial expression "I know a hawk from a handsaw," he indicates that he remains mostly in control of his faculties and that he can still distinguish between like and unlike things.