You are allowed to move the Mission Models that start out in Base (11 of them) at ANYTIME during your match, including the 1 minute, minimum, setup time.
Technically, you need a stand and they need to stay in view of the Referee at all times. Some tournaments will provide a Stand and some will not. Confer with your individual Tounament Director to see what will be available at your event. If you want a specific stand, you can bring your own usually (again consult with your TD).
As a referee, I will usually take custody of Mission Models that start out in base and that the team does not intend to use. Not all referees are prepared to do that, though.
If you store anything off the Field, the team should place them back into Base when the match ends. Most important of all, do not remove the Mission Models from the competition area! We need them for the other matches.