If one has to choose just two important quotations from the entire book, it is best to stick with quotations related to the book’s important themes. Two key themes are class struggles and loss of innocence.
The first quotation is related to class struggles. The book’s main plot focuses around two rival gangs, the Greasers and the Socs. Both gangs are based on social class. The Greasers are poor, and the Socs are rich. They hate each other because they do not understand each other. When Ponyboy meets a Soc girl named Cherry, he learns that while there are significant differences, the two groups do have some things in common.
Maybe the two different worlds we lived in weren't so different. We saw the same sunset. (ch 3, p. 40-41)
This quotation is significant because it demonstrates how meeting Cherry and talking to her has helped Ponyboy develop self-awareness about both himself and social class. Ponyboy is introspective and sensitive, so he watches sunsets. A sunset is shared by everyone. It covers everyone. It is one thing everyone has in common.
The second quotation is related to the loss of innocence. When Johnny accidentally kills Cherry’s boyfriend, he and Ponyboy have to run away to the country. They discuss a Robert Frost poem called “Nothing Gold Can Stay” about how nothing in nature lasts young. When Johnny gets injured trying to save some kids from a fire, he gives Ponyboy a command right before he dies.
"Stay gold, Ponyboy. Stay gold..." The pillow seemed to sink a little, and Johnny died. (ch 9, p. 149).
It is significant that the last thing Johnny says to Ponyboy is to tell him to remain good and innocent. Growing up is certainly about a loss of innocence. Johnny lost his innocence when he killed the boy in the fight. He does not want the same thing to happen to Ponyboy. It further indicates how Ponyboy is introspective, and his thoughtfulness is seen as goodness by his friends.