If I had a chance to write my own version of the Batman mythos, I would change some things and add some things. I must say, the Batman the mythos is changed and redone once every couple of years so it can be done differently every time.
BatmanWhen Bruce Wayne was young, his parents were killed in crime alley by the criminal that would soon become the Joker. He fashioned a suit and gadgets after the bat and became Batman, Batman's costume is grey with a yellow bat symbol and black cape. He also uses other costumes such as the Freeze suit and a glider suit, his most dangerous suit in this version of the mythos is the Shock Suit which he used once, but it almost killed him and he had to change his suit to a different one for the rest of the mission.
The Joker is the criminal that killed Batman's parents, he wears a light purple coat with the traditional Joker design. Catwoman/Selina Kyle is Batman's girlfriend, her costume is the Arkham City only with a mask. The other villains have been also redesigned, including the Riddler and Killer Croc.