Actually the Bible does give a couple of clues.
First he must have looked ordinary as Judas had to identify him to the guards who arrested him. Second, his Mother was descended from King David who the Bible describes as of a fair complexion and is traditionally said to be red headed.
Would that make her "The Virginger Mary"?
That is correct. And descent from a wife of a Hittite..Uriah, who David killed to get her.