Audience Surrogate: He's the first viewpoint character and retains the POV for most of the first book. Also, he has a much milder personality, not to mention being saner, than most of the other prominent teenagers except perhaps Violet.
Last Name Basis: She originally chose to be known as Miss Blake, with Violet as a fallback nickname. Most of the time she's just called Violet, or Violet Blake.
Miss Exposition: She knows all about art. This is helpful when you're in a world made from paintings.
The Ojou: Several of the characters are from rich families, since getting one of the eighty berths on the Mayflower was a matter of having the right connections or enough money to get the right connections. Violet acts the part, though.
And I Must Scream: Billy's consciousness doesn't shut down when he sleeps (for some reason), and that extends to the "sleep" induced by suspended animation. So he spent five hundred years immobile, alone, deprived of all sensory input. This eventually slowed down his sense of time so much that he was catatonic for a while after the survivors woke up.
Go Mad from the Isolation: While stuck in And I Must Scream for five hundred years, he went mad after less than a year. Then eventually back to sane. Then mad again, and continued to flip-flop until "the definition of madness became irrelevant." Eventually his brain went so nuts, that he started reading people's minds just to have something to do.
Ambiguously Brown: He's actually mixed-race, with a white father and a mother who's the first African-American president of the United States (the series was written in 2001), but his skin tone is perfect for this trope.