For longer games, I put "campaign" (75% "play style" + 25% "story ideas") before "system". That is, I start by learning what and how my players would like to play and by deciding what I want to put in the game, and then I choose a system that fits it (and maybe houserule it a little).
Short games are often another way around, because I use them to test and learn new systems myself and to teach them to my players. Thus, I read the books, find what the rules are good for, prepare a story that uses the bet parts and avoid the weakest ones. Then I go to my players with "You know, I have this fun new game, who would like to try it?". Both style and story is fit to the mechanics and we check if we like it or not.