This is a very complex task that you have been given. In order to organize your thoughts you need to do some brainstorming about each of the three men and think about how each of them behaves in regards to his desire for revenge. The three men are all foils of each other, and the theme of revenge is what ties them all together.
Ask yourself the following questions for each of the men:
1. How did his father die?
2. What actions is he taking to exact vengeance?
3. What does he say that reveals his attitude about the need for revenge?
4. What is the final result for each of the men?
Here are a few things to consider for each of the characters.
Laertes: His father has been murdered by Hamlet and he storms back from France ready to kill those responsible. He has a reckless attitude about the vengeance, claiming "grace and conscience to the profoundest pit." He has no thought of loyalty to the throne or to Heaven. He is willing to damn his soul in the process of revenge.
Fortinbras: His father was killed several years earlier in a battle against King Hamlet. Fortinbras has waited until an opportune time to seek his vengeance. Now that King Hamlet is dead, he sees that Denmark may be weak, so he gathers up a list of mercenaries (not the lawful army of Norway) to strike out. He is dissuaded from attacking Denmark by his Uncle/King, but he is still on the hunt for restoring honor as evidenced by his battle with Poland.
Hamlet: His father was killed by his uncle, and he is informed of this by the ghost of his father. He swears to get revenge, but wants to assure himself of Claudius's guilt before he does anything. He is concerned for his own soul. With all of this he is slower and more thoughtful to act. He recognizes even in himself that he might be overthinking and losing the name of action, but he can't help his nature.
In the end, Laertes is dead because he let himself be drawn into a dangerous plot with Claudius and the whole plan backfires. Hamlet is dead because he didn't kill Claudius when he had the chance, and that allowed him to live on and plot Hamlet's death with Laertes.
Fortinbras is the only one to survive and with "defeated joy" he claims the throne of Denmark. In the play, Hamlet tells Horatio that he admires the man who is the best mix of "blood and judgement." He is speaking of Horatio in the speech, but perhaps the line foreshadows the ending of the play. Laertes has too much blood (passion, energy); Hamlet has too much judgement (thinking, philosophy). Does Fortinbras then, in some way, have the best balance of the two in order to accomplish his goals?