This is a good question. Knowing good quotes allow you to digest and really understand a book. Also the way a story begins is very important. So, knowing something about chapter one is essential. In light of this, let me give you a few important quotes.
First, Nick, through whose eyes the story is told, is immediately a sympathetic character. We can tell he is so by his non-judgmental attitude. This is important, because he will be able to withhold judgment when others judge. This makes for a more reliable author. Right from the beginning he says that non-judgment is one of his dearest principles. He says that father gave him this advice:
‘Whenever you feel like criticizing any one,’ he told me, ‘just remember that all the people in this world haven’t had the advantages that you’ve had.’
Second, Daisy, one of the main character of the novel, says something very odd. She says that she hopes that her daughter will grow up to be a fool. This shows how women are viewed and the vacuous worldview of the wealthy who are depicted in the novel.
All right,’ I said, ‘I’m glad it’s a girl. And I hope she’ll be a fool—that’s the best thing a girl can be in this world, a beautiful little fool.’
A significant passage from Chapter 1 of The Great Gatsby is Nick Carraway's reflections on Jay Gatsby. This section is intrinsic to Fitzgerald's theme of the empty pursuit of materialism.
As narrator Nick states that when he has returned to the Midwest from the East, he wants "no more riotous excursions with privileged glimpses into the human heart." But he adds that only Gatsby is exempt from this repulsion because Gatsby has possessed
....an extraordinary gift for hope, a romantic readiness such as I have never found in any other person and which is not likely that I shall ever find again. No--Gatsby turned out all right in the end; it is what preyed on Gatsby, what foul dust floated in the wake of his dreams that temporarily closed out my interest in the abortive sorrows and short-winded elations of men.
In this passage Nick outlines his story of Jay Gatsby--the great Gatsby--whose idealism and love do not allow him to perceive his own folly: he pursues wealth as a means of retrieving his dream of love with a beautiful but careless and selfish young woman. Even when he re-invents himself and becomes "his Platonic conception of himself" (Ch. 6), Gatsby stands in the rain watching for his love, waiting for an illusion.
It is this self-absorption and materialism of the wealthy Easterners that drives Nick back to the Midwest. He returns to where he feels people still have ethical values, back where wealth and social position do not consume people (as has been the case with the Buchanans, the Sloanes, and so many others who live in East Egg and pursue the "foul dust" of materialism with no concern for the lives of those less privileged than they). Theirs, too, are short-lived "elations": the empty joy of wealth, the elusiveness of an insincere life, and the misdirected pursuit of an illusory material dream, "the service of a vast, vulgar, and meretricious beauty" (Ch.6), the empty American Dream.