Just a quick philosophical note, while thinking about my games and my gaming.
You character is cool because of what you do in play, not because of what your character is.
Some people try to craft a character that's special, and expect special in play to follow. Some people design characters who, perversely, are special in the way that they don't do things - loner types, the guy who holds back information, the guy with the special gear he won't deploy, etc.
My philosophy is that your character is special because of actions, not design and description.
Your character can be unique, special, and interesting. But what makes that unique, special, interesting character cool, memorable, and enjoyable to everyone at the table is what you do.
That's the philosophy I keep in mind and generally try to encourage in my games. Don't tell me about your character, tell me what you're going to attempt, we resolve it, and that is where cool will emerge from.