You have not specified which specific performances you have watched, but many famous actors have played Hamlet
on stage and screen. Some famous performances include Laurence Olivier, Richard Burton, Jude Law, and Ethan Hawke.
Over the years, different actors and directors have approached the character of Hamlet
in unique ways. Kenneth Branagh directed himself in his 1996 film version of the play. The staging of this soliloquy
is visually interesting as Branagh speaks to himself in a mirror. In a clip of a different production, provided by the Almeida Theatre, Andrew Scott is truly alone on stage. He wears all black, and there is no visible set. This allows Scott's acting and Shakespeare's words to be the main focus. The RSC's 2016 production (which toured in 2018) is full of drums and color. Paapa Essiedu received critical acclaim for his performance as Hamlet. In his soliloquy, we see his pain. His emotions are contrasted by the bright paint covering him and the set.
Of course, naming which actor’s performance you like the most is largely a personal decision. Acting involves emotion, so your feelings should be considered. How does each performance make you feel? Does one actor’s delivery of the speech evoke sadness or empathy in your? Does one actor make you laugh? Actors should be connecting with the audience, and as you watch these performances, you are the audience. That said, your teacher will likely want you to back up your answer with some explanation and reasoning, so you should consider why an actor makes you feel the way you do. Does the tone of their voice make you feel a certain way? Do they seem to be giving an honest or enthusiastic delivery of the words?
Aside from the acting itself, you can also analyze the other elements of the performance, such as set and costume. How does the way the actor is dressed affect their character portrayal? Do the other elements on stage enhance the performance, or distract from it? These are all questions you can consider as you try to determine what sets your favorite performance apart.