I would pick Ponyboy for the character that encounters challenges. You could pick and defend just about any character in the novel, but Ponyboy is the main protagonist. Most of the conflicts and challenges surround him.
One challenge that Ponyboy encounters is his social ranking. I'm not talking about where he ranks within the Greaser gang. I'm talking about his socioeconomic standing. Hinton does a nice job of polarizing the Greasers and Socs in a variety of ways. The number one way being a monetary division. As a Greaser, Ponyboy is poor. He's from the poor part of town and looks the part. It makes him a bit of an outsider at school and school events. More specifically, his economic status affects a possible romantic relationship. Ponyboy has legitimate feelings for Cherry; however, their relationship is sorely strained by differences between their social circles. Ponyboy is constantly challenged to see beyond his economic standing. Of all the Greasers, Ponyboy has the greatest chance of success. It's why Johnny tells him to "stay golden."