What are the advantages or disadvantages to Hamlet agreeing to get revenge on his uncle, Claudius?

Well, he doesn't want to be King, therefore, Claudius' death doesn't give him any type of political advantage. Hamlet's desrie is to return to his studies....... seeking revenge against his father's murderer is simply revenge.

The disadvantage comes from Hamlet's own hesitation. Once the ghost told him of Claudius' guilt, and as soon as Hamlet set himself upon extracting revenge, he needed to act. But he didn't. He didn't take immediate action because he wasn't really a man of vengeance. In the end, the disadvatage of waiting and imperfect timing caused the deaths of many men...... including Hamlet.