I was vaguely thinking of answering this question in a clever way by saying that Minnie Wright is the central character, even though she doesn't appear. However, I will go for the much more sensible answer of Martha Hale, who is the character that the story opens with. This is because it is Martha Hale who tells us more about the reality of Minnie Wright and her background, and how she changed being married to John Wright and suffering the isolation and loneliness that was part of her life. Note her comment on John Wright as a character:
"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." Her eye fell upon the cage on the table before her, and she added, almost bitterly: "I should think she would've wanted a bird!"
Martha is important because of the way that she allows us to have a much fuller picture of the Wrights and the way that Minnie was transformed. Note also that she is the character who begins to remove any trace of evidence that could possibly be used to indicate that Minnie Wright was disturbed or suffering anxiety. This can be seen in the way that she re-sews the bad sewing that Minnie Wright did that was in such contrast to the rest of her neat sewing. Martha Hale therefore is the most important character because it is she that is used as the primary vehicle for expressing the theme of female solidarity and it is she that influences Mrs. Peters.