Nope. Nothing in the character creation system needs to be unlocked.
The only things that need to be "unlocked" are clothes, but you just buy them at the stores.

Do you have to unlock the hair and such?

I'll be waiting for the sale now.

I recommend getting SR3 first, since it's a better game, and it's better to play the games in order (1 and 2 were pretty much an entirely different series).
You can usually get both games for around $5 on a sale :)

I wish i had this game, so i can make my own character

Thanks :D

This was one of my two main characters in the game. The other one was my Joker character :)

Woah, really cool!