I'll have a go at your question. Hamlet, without a doubt, is intelligent, perceptive, and insightful. This fact is evident throughout the play. As such, he seems to value and use different kinds of knowledge.
First of all, he is an empiricist. He is the "observe'd of all observers." Through his careful observation of others, he is able deduce Claudius' excessive drinking, his mother's too sudden fall for Claudius, Ophelia's betrayal, Polonius' and other of king's spies' espionage, and Claudius' guilt (as he reacts to the Players). He makes use of these observations as he navigates throughout the corrupted currents of the court, deftly managing Claudius' attempts to contain him.
Hamlet also possesses cultural knowledge: he knows the Bible well (Notice his allusions in his conversation with Polonius in Act 2); he knows Greek and Roman mythology; he is well versed in drama; he is astute in history and current events. Hamlet uses this knowledge to set a trap for Claudius, to elude Polonius, and to connect with Horatio.
He is also rational and logical. Look at his most famous speech, "To be or not to be." It is a well reasoned argument, posing and answering the question of why we "bear the whips and scorns of time" when we could our "quietus make with a bare bodkin." The speech is a beautiful piece of rhetoric, which outlines the pains of living, the temptation of suicide, and the fear that causes us to cling to that which we know rather than to travel to that "undiscovered country, from which no traveller returns." Other examples of his logical mind can be seen when he shows Claudius in Act 4, Scene 3 how a "king can progress through the guts of a beggar," and in Act 4, Scene 4, when he analyzes the nature of thought, man, and action and the relationship of all three. More examples of this type of analytical thinking occur in Act 5 in the graveyard scene and much earlier in Act 2 with Rosencrantz and Guildenstern, with Hamlet's speech "What a piece of work is man." Perhaps it is this knowledge that Hamlet most values. And perhaps it is this type of thinking that leads to certain philosophical conclusions about action, man, death, life that leads us to judge Hamlet as a prince of thought rather than a prince of action.
Most of all, perhaps, Hamlet is intuitive. He lets his conscience guide him, which at times causes his most pronounced conflicts. He is torn between his love and loyalty to his father and his obvious reluctance to murder. He attempts to operate with conflicting values, attempts that have tragic consequences.
Concerning your difficult and multi-layered question about Shakespeare's Hamlet, I suggest the following:
- Hamlet values broad, general knowledge and abstract ideas. See his soliloquy in Act 1.2.129-159, in which he contemplates the state of the entire world and of existence; and his "To be or not to be" speech in Act 3.1.56-90 in which he contemplates existence--to be is to exist.
- The source of Hamlet's knowledge is contemplation. See the above, again.
- His motivation for acquiring knowledge is predominately for its own sake. Power doesn't seem to be important to Hamlet, and he already has freedom, unless you look at it from the perspective that he wants freedom from his situation or the trials of life, etc. That is a possibility. I'll leave that to you.
- Hamlet uses knowledge to gain more knowledge (more contemplation) or to know how to behave or proceed.
I write the above in an effort to help you out. I am not an epistemologist (studies the nature, etc., of knowledge) and was not even going to tackle this question until I received your email. I make no guarantees, whatsoever, and I'm hoping another editor with a better answer answers the question for you!
But, in the mean time, I'll add a passage from the enotes Study Guide on the play, as well:
One response to this question [why Hamlet delays his revenge] stresses Hamlet as a man of thought and words, as opposed to deeds. Shakespeare's Danish prince is one of the most intelligent protagonists in tragic drama. Unlike many other Elizabethan revenge tragedy heroes, Hamlet is given to philosophy and abstraction. At times, it seems that the play is less about Hamlet taking action in the external world, than it is about his grappling with the key existential problems of human existence. From this standpoint, Hamlet does not act immediately because he is too preoccupied with analyzing his situation and himself in the broadest terms imaginable.
Between what I've written and the Study Guide, I hope this is of some help.