We usualy start with the story, of course, very often, ideas come up while the character is being drawn and story can be changed a little.
Some character pictures have the story perfect as they evolve. Someothers sorta just go blah.
i.e. Vermyn N has a great evolution sequence showing how he goes insane from not being able to do anything bad (with the Bangers). I can see him going to either GHEIST or Nightmare one day.