How is Hamlet a typical Renaissance prince?

Remember that the Renaissance was fairly young when Shakespeare wrote Hamlet, and there were no clearly defined rules for what was considered "typical".  Hamlet, however, is different from Fortinbras and Laertes who are quick to action and have a "Damn the torpedos, full speed ahead" (to borrow a famous line from actor John Wayne) attitude with which they tend to act first, then think. 

Hamlet is just the opposite, in fact, the antithesis.  Hamlet thinks all the time, too much probably.  Also, Hamlet is a very well-educated and intelligent prince, a quality that makes him Renaissance-like.  Hamlet can be a man of action when action is immediately called for, as he proved when he fought the pirates, an event he describes in his letter to Horatio in Act 4.6. 

Hamlet also questions the world around himself.  He ponders philosophical matters, especially in his soliloquies, such as the meaning of life and what motivates people.  Nor does Hamlet readily accept the fact that the Ghost of his father is truly his father's spirit.  Even though at first Hamlet says, "It is an honest ghost" (Act 1.5), he later decides he must perform a test to see if the ghost was real or a demon meant to lead him astray.  Testing truth was a quality of Renaissance thought and evident in Protestantism, which is represented by Hamlet's university in Wittenberg.