How would I get the current player's appearance ID?

You can throw this in starterGui and it will grab everyone who enters AppearanceId. If you put it in ServerScriptService you are going to have to add a Wait() or WaitForChild() Function into the script because ServerScriptService runs before Character is loaded

local Players = game:GetService("Players")
function onPlayerAdded(player)
local character = player.CharacterAppearanceId
print(character)


end



for _,player in pairs(Players:GetPlayers()) do
     onPlayerAdded(player)
end