There are too many examples of racism and "racist" quotes in the book to count. I will try to give you a few broad examples that will allow you to choose specific quotes.
Considering the historical time the book takes place as compared to our world today, there are several quotes that could be considered (by to today's standards) "racist" quotes. The use of the n-word is prevalent throughout the book and this word holds an immediate "racist" and demeaning connotoation. Though it was certainly more commonly used in the 1930s than it is now, even then it was considered offensive. If you were to skim through a couple chapters of the book you will undoubtedly run into several examples of its use.
If you wanted to show the difference between racism then and now, you could find examples of the use of the word "negro" as a lable for black people. Today, this word is not as offensive as the n-word, but it does hold a negative and certainly a demeaning connotation. At the time the book was set, however, it was acceptable.
Finally, if you re-read through the trial scenes (Chapters 16-20) you will notice the very racist attitude of Bob Ewell and of course, how it has affected his daughter Mayella. Also look at the way Mr. Gilmer (the prosecuting attorney) cross examines Tom Robinson. He calls him "boy" and treats him in a manner that could be perceived as racist.
The most meaningful quote that I can think of at the moment is spoken by Atticus in Chapter 23.
Atticus tells this to Scout and Jem after they start telling Atticus how unfair it is that Tom Robinson was declared guilty because of his race. This is Atticus's major opinion concerning the prejudices that white men have towards black men in the novel.