Poe chose Montresor as his narrator because he is a madman, and madmen make good narrators.
Madmen are unreliable narrators, because they think they are clever and doing the right thing. Montresor is an example of this. He thinks that killing Fortunato is the right thing to do because he has insulted him in some way, even though the insult is likely small and imagined.
The thousand injuries of Fortunato I had borne as I best could, but when he ventured upon insult I vowed revenge. You, who so well know the nature of my soul, will not suppose, however, that I gave utterance to a threat. At length I would be avenged…
Although Montresor would surely tell you he is as sane as you or I (if he were a real person), he clearly is not playing with a full deck. You do not murder someone because he has insulted you. If Fortunato had really done something to Montresor, he would not have turned his back on him or gone into a crypt with him. The fact that Fortunato suspected nothing is evidence that the “injuries” and insults are imagined or minor. Montresor is nuts.
Why choose someone who is crazy to tell your tale? Well, crazy people are more interesting. This story would have been pretty boring if it was about one friend showing another friend a cask of wine and asking him his opinion of it. I doubt that story would be read a hundred years later. No, a real story has to have a hook. A suspenseful story is when one of those men is plotting the murder of the other.
I must not only punish but punish with impunity. A wrong is unredressed when retribution overtakes its redresser. It is equally unredressed when the avenger fails to make himself felt as such to him who has done the wrong.
Did I mention that not only does Montresor have to kill Fortunato, but he also has to get away with it? So he gets rid of his nosy servants (he tells all of his servants to make sure they stay home because he won’t be there, knowing they will leave), and goes out on the town for carnival.
Montresor is a good observer of human nature, as all madmen seem to be. Consider how well he knew his servants! He also knew that Fortunato’s guard would be down at carnival time, and others' would, too. He even lowers Fortunato's defenses by suggesting that Fortunato leave, that he will get someone else to look at the wine.
“My friend, no; I will not impose upon your good nature. I perceive you have an engagement. Luchesi—”
“I have no engagement;—come.”…
“Let us go, nevertheless. The cold is merely nothing. Amontillado! You have been imposed upon. And as for Luchesi, he cannot distinguish Sherry from Amontillado.”
Montresor knows that if he suggests that someone else should look at the wine, then Fortunato will want to look at it. It’s human nature. He does not want to miss out.
Another reason Montresor is a good narrator is because he thoroughly creeps the readers out, but he makes us look at ourselves. Does Montresor have a conscience? After he bricks Fortunato in, and he starts to realize what has happened to him, he panics. He screams to Montresor to let him out, hoping it is all a sick joke.
Montresor does not let him out, but does he have a conscience after all? He calls to Fortunato—to make sure he is dead. Yet, look at his reaction.
My heart grew sick; it was the dampness of the catacombs that made it so. I hastened to make an end of my labour. I forced the last stone into its position; I plastered it up.
You can interpret this as an attack of conscience, even though Montresor attributes it as the catacombs. It is revealed that he is looking back on the incident, which implies grief and remorse, because “half of a century” has passed. The last words of the story, “Rest in peace!” can be interpreted ironically, or genuinely. The entire thing seems like an attempt at a justification, not to the reader, but to himself.
Can you be mad and have a conscience? Absolutely. In fact, psychopaths often feel that they are compelled to commit heinous acts, and then feel remorse afterwards. Sociopaths do sometimes commit their horrible murders without caring. Which one is Montresor? It's up to you to determine.
It could be that Montresor has no conscience, and the last sentence is ironic. However, he could actually feel some sympathy and remorse for what he has done. He killed with impunity. That was what he wanted. There is no reason not to feel remorse as well for Fortunato. In Montresor's mind, he deserved to die. Yet Montresor can still be sad that he is dead.
The ending of the story is open to interpretation, depending on your view of human nature. What is not open to interpretation is that Montresor is mad. Poe chose him because madmen make good murderers, and murder makes a good story. We like to read about murder because it is exciting, and because stories like this tell us more about ourselves. In this story, we learn to be careful who we trust. Sometimes people who seem normal are far from it.