There are a lot of things to consider when you are building a new character. What is their personality going to be like? What background do you imagine for them? What role will they fill in the group? Which mechanics (skills, stunts, etc.) are they going to be high or low at? What unique powers do I want to pay for? How will the other players view this character?
Character design can be a lot of fun, and most systems spend a lot of time and money dedicated to this stage of roleplaying. Most people have an opinion or two on this subject, so I thought I would share my 2 bits on the subject.
Choosing a Concept
I like to start with a character concept, something that would be fun to play, and then see about making it fit, though I do not begrudge anyone that starts with one of the next 2 sections below.
The 2 main things to consider with concept are the setting and your own personal goals. The setting of a game is typically designed for a certain type of character: adventurers in D&D, samurai in L5R, semi-normal people in Cthulu. A large man with a crossbow is going to feel different in each of these 3 settings, and thus a setting will affect what sort of concept you want to build.
Personal goals are also important in choosing a concept. If you want to challenge yourself to play something new, choose a concept that you never play. If you just want to have reliable fun, choose a concept that you enjoy playing. Your creativity is only going to be limited by the next step.
Making it Fit