At the end of Shakespeare's Hamlet, it is said by Fortinbras, the prince of Norway, that Hamlet would have made a good king. Justify this statement with qualities that suffice Hamlet being King if he survived, including three examples from the play as evidence. Please include quotes, citing acts and scenes..

In order to be King, Hamlet would have to be proven mentally stable first and foremost. So establishing Hamlet's sanity (and feigned madness) would be crucial. He certainly spends a great deal of time making people believe that he's insane in order to further his primary goal of killing Claudius. However, underneath it all, he always returns to a place of reason, if only in his own monologues and in speaking with Horatio. One place where Hamlet's sense of reasoning is clear appears in act 3, scene 2 when he lays a trap for Claudius by devising the "play within a play" to test his guilty (or not-so-guilty) reaction. This took quite a bit of planning and also some interpretative skill as he judged the reaction of his uncle. He even directs the actors with great precision:

Speak the speech, I pray you, as I pronounced it to you, trippingly on the tongue. But if you mouth it, as many of our players do, I had as lief the town crier spoke my lines. Nor do not saw the air too much with your hand thus, but use all gently, for in the very torrent, tempest, and (as I may say) whirlwind of passion, you must acquire and beget a temperance that may give it smoothness. (3.2.1–8)

This precision is not directed by an irrational thinker. Hamlet proves himself quite steady and meticulous in his plans.
Hamlet does not react impulsively—most of the time. When the ghost of his father tells him what Claudius has done, Hamlet seeks to first establish the credibility of the source. Once he is convinced that the ghost is his father's spirit, he knows that he must seek revenge on Claudius. He carefully weighs out his plans, trying to then be certain that Claudius is guilty. After the play, he has this certainty but still doesn't kill Claudius, because he finds him in the midst of prayer. Hamlet notes,

Now might I do it pat. Now he is a-praying.And now I’ll do ’t. And so he goes to heaven.And so am I revenged.—That would be scanned.A villain kills my father, and, for that,I, his sole son, do this same villain sendTo heaven. (3.3.77–82)

Hamlet wants to make sure that he completely thinks through this important decision. His one rash act is the murder of Polonius, whom he didn't actually plan to kill. He was in a bit of an emotional state when this happened, which could explain the change of character.
Third, Hamlet is intelligent. He navigates the complicated relationships of his uncle/stepfather, mother, the ghost, friends who try to betray him, and Ophelia without getting himself killed (well, at least until he achieves his revenge) and without deviating from his plan. He single-handedly concocts a plan to illuminate the deception of Claudius. Hamlet creates an alternate persona to throw everyone off track in order to propel his revenge without raising too much suspicion. He plays with words masterfully, and Polonius notes the craft of his skill in act 2, scene 2: "Though this be madness, yet there is method in’t" (2.2.217–218). His speech about whether to live or die shows calm and deep musings about why people often choose a life of suffering.
Based on these credentials, you could build a solid paper defending Hamlet's suitability as king.