I have to write a essay on the strengths and weaknesses of Hamlet in the play "Hamlet". I was thinking that one of his strengths could be his...

I would agree that Hamlet looks at life in a more philosophical manner than most protagonists of revenge dramas. He is also more empirical about deciding whether or not to kill Claudius than the average character in a revenge play. He seeks to confirm that Claudius murdered his father instead of rushing out to kill him on the word of a ghost. Because he thinks so deeply about reality, appearance and death, because he is so self-reflective, Hamlet has sometimes been called the first modern hero. He has also been attacked as indecisive, but one can question whether it is "indecisive" or, instead, prudent, thoughtful and morally sound to ask questions before you kill another person. 

Critic Rene Girard writes eloquently in defense of Hamlet as a character who struggles with and calls into question the whole idea of revenge that the play revolves around. He writes in a chapter entitled "Hamlet's Dull Revenge," in Theatre of Envy that Shakespeare wanted to undermine the revenge tragedy genre. Girard called Hamlet

the most brilliant feat of theatrical double entendre.… he will denounce the revenge theater and all its works with the utmost daring without denying his mass audience the catharsis it demands … (273)

To do this, Shakespeare must make Hamlet a contemplative person, a thinker and questioner of his society. 

Within the play, Hamlet expresses deep questioning, as you note, in his soliloquies, such as in his "what a piece of work is man," or "to be or not to be" speeches, and in act five, scene 1, when he enters into conversation with the grave diggers, as well as when he questions the sincerity of the mourners at Ophelia's grave. He is constantly questioning appearance versus reality, so it should easy to find examples of that in the play: I have provided the link to E-notes quotes from the play below.