I generally don't do sign ups at all because I don't want to miss out on a potentially great cosplay while at the convention.
If I were you, I'd offer sign ups publicly for one day of the convention. Do it however you feel is fair. If you want to create a public image of first come, first serve, that way you won't create a suspicion about rejecting cosplayers over quality, then that's what you do. Then, you hold off on making an announcement that you're fully booked, until you get a lot of cosplay requests that you're happy with. Once you're satisfied, take the first people who publically signed up and give them shoots on your announced day. Then, if there are cosplays that are really awesome that you know you can't miss, but let's say they didn't respond quick enough, or see your post, you can secretly schedule those for other days of the convention. This way, no one feels like their cosplay wasn't good enough because you went with a first come first serve policy, but it also allows you to make sure you get the cosplays you want by privately scheduling those shoots on different days. 1 day for public, the rest for private, or some combination of the 2.
I hope this resolves the dilemma you're starting to have.