In The Absolutely True Diary of a Part-Time Indian, what are the things that Junior would want the most that a person can give him?

Release from the world's limitations would be something that Junior would want from another person.
The removal of limitations is something that defines the arc of Junior's narrative. He finds himself as a "part-time" Indian because he wants more. Junior seeks to be released from this world of limitations and looks for this experience in other people. Junior sees this in Penelope. When she speaks of wanting to go to Stanford and creating something lasting that represents beauty, it triggers specific feelings inside Junior. He longs to escape the life of "the Rez" and seeks something more than what is around him. His whole desire to go to Reardon is rooted in wanting to expand his horizons. Junior sees Penelope as trying to be more than the world around her, something he identifies in himself.
At the end of the novel, when Junior is playing basketball with Rowdy, they are not keeping score. Their friendship has transcended limitations. They have moved past the social limitations that divide life on the reservation from life at Reardon. They have moved past the differences in their own realities. They have even moved past the constraints of keeping score. In this moment, Junior is happy because he has moved past judgments and social definitions. In his relationships with Rowdy and Penelope, Junior yearns for the world's limitations to disappear.