In the first chapter of To Kill a Mockingbird, Harper Lee fully develops her main character of Atticus, Scout, and Jem Finch.
We learn about Jem first, when we hear that he broke his arm when he was thirteen.
When it healed, and Jem's fears of never being able to play football were assuaged, he was seldom self-conscious about his injury. His left arm was somewhat shorter than his right; when he stood or walked, the back of his hand was at right angles to his body, his thumb parallel to his thigh. He couldn't have cared less, so long as he could pass and punt. (ch 1)
This tells us a lot about Jem’s character. We know he is not vain, but he does enjoy playing sports.
We are also introduced to the other members of the family. Scout does not describe herself first. She describes Jem, Atticus, and Calpurnia.
The Finch family itself is pretty small.
Atticus Finch, went to Montgomery to read law, and his younger brother went to Boston to study medicine. Their sister Alexandra was the Finch who remained at the Landing: she married a taciturn man who spent most of his time lying in a hammock by the river wondering if his trot-lines were full. (ch 1)
We learn quite a bit more about Atticus, who is really a remarkable character. His first two clients were "the last two persons hanged in the Maycomb County jail" (ch 1), yet he still tried to defend them even though they were stubborn. Atticus is principled and mature.
During his first five years in Maycomb, Atticus practiced economy more than anything; for several years thereafter he invested his earnings in his brother's education. (ch 1)
Atticus cared enough to put his brother through school instead of spending the money on himself.
Calpurnia is another member of the family, the housekeeper, and she serves as the mother figure.
Calpurnia was something else again. She was all angles and bones; she was nearsighted; she squinted; her hand was wide as a bed slat and twice as hard. ... Our battles were epic and one-sided. Calpurnia always won, mainly because Atticus always took her side. (ch 1)
From all of these descriptions, we learn that Scout, the narrator, is intelligent and precocious. She does not know everything or see everything as an adult would, but she is perceptive and able to tell us a lot about family history. In chapter 2, we learn that Scout can read and that she does not back down. Miss Caroline punishes her for arguing about already knowing to read. Scout also finds it important to educate Miss Caroline about the social order. Of course we also learn that the Finch children have active imaginations and are fascinated by the legend of Boo Radley.