I did not read her letters, and these are my assumptions of her based on her books and some general known trivia.
She grew from Catherine to Emma, from Emma to Lizzie, from Lizzie to Anne, and from Anne to the full-fledged Jane Austen. She always possesed a great wit and carried herself proudly, but lacked experience and self-observation. She loved her only sister, teased her brothers, and adored her father, even though she was aware of their faults. She experienced love, but loved her freedom more.
PS: It would be great to pick more favourite adaptations, 2-4 perhaps? Otherwise it might be quite an easy victory (but I admit that there is bias, funnily, a half of the adaptations I watched are based on Emma).