Playing with the System Extremes in attributes, advantages, disadvantages and skills can be used as a central character feature. Think about how such an extreme characteristic would affect the PC and his interactions with other people. Experiments with game mechanics can sometimes yield interesting characters, although they can produce abusive designs, too. Be prepared for the GM to reject experimental designs in a campaign game. Campaign Considerations Profession can be a good starting point, since it will define a set of skills and indicate which attributes are important.
Background is for the player who likes creative writing.
Start with the character's childhood, and create a biography for him up to the point where he enters play. The PC's parents, teachers, and early experiences will mold his character and dictate what skills he is likely to learn. Party composition is sometimes important. I find this type of character one-dimensional and unsatisfying to roleplay, although some have taken on a life of their own. On the other hand, a party that already has several big, dumb fighters probably doesn't need another one . . .