Lots of great advice. I'm not going to offer any advice, just an experience of the last time I tried to feed 60+ people. My only job was the meat. Three 8 lb bone in pork sholders, three 8 lb chuck roasts. Cooked to perfection and pulled. Problem is that this was the main dish, and for the most part people didn't get to it. It was put out last. With drinks and sides, I'd estimate I was 70% too much meat. So you really need to access your audience and sides and beverages. It throws a wrench into x lb per person calculations.
DK
15 racks sounds like a safe approach.