As of now, there is a basic default appearance for each of the five main monster characters (skin and hair color, racial makeup.) That also applies to whichever one you decide to play. The exception is the demon, who can choose whatever appearance they prefer from a list of options. You’ll then get to choose gender and personal style.
I may or may not expand appearance options if there’s more interest in them. I am seriously considering making every non-player character a set gender, and letting people who aren’t interested in dating that gender skip those romance options/date storylines if they want. (@Elfwine made a good case for that here - Surviving High School: Freshman Year (WIP))