Sometimes I start with the angle, like, Arthur hasn't had sex since the mutant headhunters dragged off his boyfriend, and now someone's trying to seduce him in the hold of an alien ship. The angle is "first time since" and all the rest is window dressing (you know, that plot stuff). I build the rest of the story around that. In that case, I'd be starting with a situation and letting the character grow from it, and building the setting as needed.
Sometimes I start with a setting, as I'm doing with "Poppies...", and let the characters grow out of that, and once I have them, I try and figure out the angle. That seems to take a little longer.
Sometimes I have the characters and not much else, but if I form the characters really well, I can know what the angle is almost immediately. With the best characters, a cornucopia of angles overflows onto the page, and I can pick and choose.
I'm not sure if an Angle is the same thing as a Gimmick. Sometimes, maybe. I have another idea, that I also want to try and write for the BLE deadline; I want improve my chances of acceptance by submitting an sf story, like I usually sell to them, along with the historical story. When having dinner with feklar and missionista after the Bluestockings reading, I decided a time travel story would be neat, and I thought of a twist right then and there. So for that story, I have a gimmick. I need characters, and from them will be born the Angle. I wrote the opening paragraph this morning. Hopefully I can get further than that.