Like @elyss, I usually start with characters, but I always have an idea in mind when I create them. I build the story and world around the characters because I think It's more important to have good characters over an interesting world. A lot of the time fantasy shows up in my stories because there is more freedom in the genre. I'm a planner, so I will usually outline a story before I begin to do actual work on it.
A good way to keep personality flaws in mind is to look at personal flaws or flaws of the people you know or even in media. I have a character who a a trait that is a double edged sword; He is the leader of the group and feels responsible for everyone else in the group. He feels like he's the only one capable of protecting the others and that cause him to distrust the others' ability to take care of themselves. It's not as though he doesn't respect them, just that he's always been the one in charge. I did not come up that flaw on my own; I actually grabbed it from Superman. As the strongest man in the world, he feels like it's his responsibility alone to protect the planet, even though he is a part of a league of heroes, whom he respects, who can save the world also.