Loads of places to look here. One of the most impressive places to quote from I would argue would be one of the least-appreciated scenes in the play: Act 4, Scene 3. This starts off being a debate between Malcolm (playing devil's advocate) and Macduff about what makes a good king.
Malcolm gives a useful list (in the same scene) of the kingly virtues:
The king-becoming graces,
verity, temperance, stableness,
perseverance, mercy, lowliness,
Devotion, patience, courage, fortitude...
The two key questions to ask, I'd reckon, would be whether these virtues are embodied by Duncan and by Macbeth - and then justify that answer in the text. Duncan, even Macbeth (his murderer!) admits, is a kindly and excellent king. Macbeth, of course, doesn't get such good reports. Take a close look at the banquet scene or the scene in which Macbeth invites Banquo to the banquet: and analyse what sort of a king Macbeth has become. Is he, as the final lines of the play have it, simply a "butcher"?
When you've looked at the kings within the play, it'd also be good to look at the king it was written for. James I was fascinated by witches and demonologie (he even wrote his own book about it!) and was Scottish - a fair demonstration, most critics think, that the play was written for him. How might the play work as a play played out in front of a king?
When writing on the theme of kingship, you might want to think about what the play suggests makes a good king. Does a king need to be the rightful heir to the throne to be a good king, or are personal qualities more important? Perhaps both being the rightful heir to the throne and having good qualities such as leadership and honesty are important.
To answer this question, you might start by examining the differences between Macbeth, who becomes king after murdering Duncan, and Banquo, whose heirs rightfully assume the throne after Macbeth's death. When both Macbeth and Banquo hear the witches' prophecy, Macbeth immediately becomes intrigued by the witches' words and becomes overly ambitious to become even higher than the Thane of Cawdor, a title that Duncan, the king, has already granted him.
However, Banquo is indifferent to the witches, who promise he will be the ancestor of kings. Banquo says in Act I, scene 3, "But ’tis strange. /And oftentimes, to win us to our harm, /The instruments of darkness tell us truths." In other words, he fears the witches are instruments of the devil, and he advises Macbeth not to listen to them. In contrast, right after Macbeth hears the witches' prophecy, he starts to dream of killing Duncan and says in Act I, scene 4, "Stars, hide your fires; Let not light see my black and deep desires." In other words, unlike Banquo, Macbeth has allowed his ambitions to cloud his judgment and make him desirous of evil. The play suggests that the rightful kings--such as Duncan and Banquo's heirs--not only have the hereditary right to claim the throne but are also ethical and righteous people, unlike Macbeth, who neither has the right nor the integrity to be king.