If you mean by "self-driven" that Hamlet is independent in his thoughts and actions, many quotes are applicable. First of all, Hamlet is not easily persuaded. He does not heed his mother's advice to
Cast thy nighted colour off
And let thine eye look like a friend on Denmark.
Instead, he informs her that his clothes only reflect the melancholy he has within:
I have that within which passeth show.
Neither will he listen to Claudius's threats, insults or bribes in this same scene. In response, he ignores Claudius.
Hamlet does not even follow the ghost's mandates to avenge his death until he verifies Claudius' guilt himself. He himself decides to "put an antic disposition on" and later devices the plot to determine Claudius' guilt:
The play's the thing to catch the conscience of the king.
Another way to look at your question is to examine how Hamlet must talk himself into committing a vengeful act. No one goads him into killing Claudius; no one persuades him. Instead he convinces himself, after hearing the ghost, that Claudius is guilty and must suffer a fate worse than his father. He tells himself that he is ready to "drink hot blood" and do "bitter business" in Act 3, and in Act 4, he declares that his thoughts will be "bloody." And indeed, he does act independently when he kills Polonius, and later when he has Rosencrantz and Guildenstern killed.