To begin, I would suggest that you consider writing about the two characters that you feel you know the most about. Scout and Atticus might be good candidates for comparison and contrast, since a great deal of information about them is given throughout the novel.
It may help you get started on the writing process by first doing a Venn diagram, since it will help you organize each character's traits by determining what traits the two share, as well as what traits are only displayed by one individual. Think about the ways that Scout interacts with others, then ask yourself if her father would handle the same situation in a similar way or differently. Also, take into consideration the lessons that Atticus teaches Scout (and others) throughout the novel.
There are many ways in which you should be able to compare and contrast Atticus Finch and his daughter. Scout has a quick temper, while Atticus is generally very patient and even tempered; we see how hastily Scout tends to react to situations when Jem catches her "rubbing [Walter's] nose in the dirt." Scout also tends to judge people quickly, unlike her father; however, she is like him in that she does not understand discrimination and is intelligent.