I'd recommend your first one be a charity ride or some similar arrangement. The catered (usually fruits & powerbars, with a proper lunch in the middle) stops every 10 miles or so make a century seem like a pleasant romp through the countryside. I've ridden straight through a century fixed, satisfying but
not as much fun especially since it wasn't an actual race. I don't know of any orgs that race centries fixed although I'm sure you'd be allowed to in a USCF or other road racing setting. I'd want other fixies to race though. Road bikes win every time in a century with equal riders on anything else.