I think that you can find several speeches of Macbeth to analyze. From what I have been seeing on enotes, the most popular one of late has been his speech when he hears that his wife has died. The sense of emptiness, combined with futility and despair seems to be the most profound of speeches, one that reflects a rather pain- ridden condition regarding being in the world. This is one that I would spend some time in analyzing, as much about the existential state of human beings and Macbeth, as a character, is revealed.
Another speech I would focus on would be in Act I, sc. iii. Macbeth's openness in wondering about the witches and their implications is fairly profound, given how his character is going to develop in the course of the drama. The emotional and psychological wondering as to what will become of this "soliciting" reflects how Macbeth starts off as a human being, filled with doubt and insecurity. This is in stark contrast to what he is going to become at drama's end, but being able to assess this vision of Macbeth with what is presented when he speaks of his wife's death is something that can give a very rounded understanding of the character.