I would look at Mabeth's relationship with Duncan, his relationship with his wife and his relationship with Banquo.
If you think about the time period, a subject's duty to his king, especially one that has just honored him, Macbeth's treatment of Duncan isn't just a murder, it is an extreme betrayal. Also considering that Macbeth was Duncan's host, someone who was supposed to protect him, there is definitely a lot to be explored here.
Characterizing the relationship between Banquo and Macbeth in the first act - close friends, comrades, fellow soldiers etc. Macbeth turns on someone who is supposed to be his confidant in previous situations.
Lady Macbeth illustrates that she is a strong woman, one who wishes to be Macbeth's equal in Act 1 and 2, but Macbeth forsakes that relationship by keeping her in the dark about the subsequent murders for the rest of the play.
I hope that helps. Consider reading up on the analysis of these characters at the links below.