I'm glad you asked, as I do have a favorite character in Leif Enger's first novel, Peace Like a River; however, there are many ways to define "best" and every reader will not connect to the same character. I will define "best" as the character I feel the most connection to: Swede Land.
Swede is the rather precocious daughter of Jeremiah Land, and she has two brothers. She is a writer and she she is fiercely loyal to her brothers. While she can be silly and ridiculous at times, I would want her on my team because she is creative and she perseveres. She is a delightful mix of charming naivete, quick wit, and keen intelligence.
Other readers might find more connection to Davy because he defends his family unapologetically and is then bold enough to escape from prison and take off on his own. Or perhaps they will admire the faith and faithfulness of Jeremiah Land, a man who breathes miracles and talks intimately with God. Roxanna is a woman who has been hurt often and deeply but still has the capacity and willingness to love with all of her soul, and some will identify with her.
Many more will probably connect to Reuben Land, the narrator of the story and the recipient of two breath-taking (or perhaps breath-giving) miracles. He has a wonderful voice full of wonder and questioning as his family leaves everything they own in the quest to find Davy. Reuben loves his family, even when he does not understand them. He says of his father:
Many a night I woke to the murmur of paper and knew he was up, sitting in the kitchen with frayed King James--oh, but he worked that book; he held to it like a rope ladder.
We experience this story through his eyes and hear it through his voice, so he is the character many will consider the "best."
If this is a question you have been asked to answer for class, I would encourage you to decide what "best" means to you and then determine which character most suits your definition.