I always like to go out on a limb with questions like this, because really, you can choose any character you want to as long as you can find evidence from the text to back up your conclusion. So I am going to argue that actually the most important person in this story is a character that we never actually meet, but we only hear about. John Wright is a character who dominates the entire short story with his iron will and strength, and of course in him we find the solution to the murder mystery that we are presented with.
Note the way in which he is described by Mrs. Hale:
"He didn't drink, and kept his word as well as most, I guess, and paid his debts. But he was a hard man, Mrs. Peters. Just to pass the time of day with him--" She stopped, shivered a little. "Like a raw wind that gets to the bone."
It is thanks to her marriage with such a man that Mrs. Hale remembers Minnie Wright changing so dramatically, and her thought that Minnie would have wanted a bird to brighten up her home indicate the kind of oppressive regime that John Wright imposed on his wife. The subsequent discovery of the canary with its neck wrung is of course perfectly in keeping with the character of John Wright, and we can understand why John Wright is such a powerful symbol of harsh, repressive patriarchal authority and therefore the most important character in this excellent short story.