We can learn a lot about a guy like Bert by examining his actions. He stands up for what he believes in and refuses to conform—even when facing jail time. Rachel, on the other hand, is weak. She's too afraid (for most of the play) to go against her father, and testifies for Brady, even though Bert is her friend-crush.
Other actions are more subtle than Bert's taking-a-stand sort. Brady's always stuffing his face with food, and Mrs. Brady is always asking him to stop, which tells us something about his insatiability (kind of like his hunger for fame), and her role as his caretaker. Nice.
The only family we see in this play is that of Rachel and her father, the Reverend Brown. Rachel mentions that she never knew her mother, so we know that it's just her and Rev. Brown. So she's completely under his nutty rule.
Also, Rev. Brown's willingness to publicly damn his daughter to hell is pretty shocking. It tells us a lot about the Reverend's character, and his extreme belief system.
The various characters' occupations reveal what is important to them. Brady has run for president three times because he has a deep need for fame. Drummond is a lawyer because he is obsessed with the truth. Hornbeck is a journalist who is like an annoying mosquito, pointing out all the flaws in society. And Bert and Rachel are teachers—two earnest folk who care about their community.