*puts nerd cap on*

I've been thinking on that and given that thousands of colonists are on board I sincerely doubt that they were shoved into the hydrogen tank of a space shuttle or any modern space-faring vessel for that matter. A modern space shuttle is out of the question, it simply isn't capable of holding thousands of people. 

I think shuttles could be used to ferry pods though. A large portion of the fuselage is dedicated to scientific equipment but could be removed to store pods instead and that would give us all a reason to be packed in a shuttle before cryo. 

As for the ship that gets us there (which should have some solution for getting us to and from planetary surfaces) would need to be a much larger construction. Something kilometers long with multiple decks and livable areas. Basically it should accommodate life on board the ship as a temporary measure until colonization begins. 

Also, Eliza doesn't have a job or technical skills so she would probably be marked as non-essential personnel and probably not be brought out of stasis until after the crew of the ship at the very least.