Don’t get your Colosseum ticket from the Colosseum. The queues can be huge and the ticket you receive is valid for both the big round thingy and the nearby Palatino… so get your ticket from the latter instead. The queue is rarely longer then five minutes, but make sure you have change as the guy who served me ran out!
Tickets at the time of writing are 11 Euros and if bought before 13:30 are valid at both sites on the same day. If you get the ticket later, they’re valid for one site that day and up to 13:30 the next, so you can do one in the afternoon and the other the next morning.