that Johnny killed him in self-defense (or defense of Ponyboy).

Bob is Sherri "Cherry" Valence's boyfriend.  He is also the Social that beat Johnny up. (We learn this through Ponyboys' retelling of the story the night of the movie). He drives a "tuff" blue Mustang, wears a lot of rings (a clue that tells us he was responsible for hurting Johnny), and likes to bully others. He directs another social to "give the kid a bath" in the scene at the park.  That social then pushes Ponyboys' head under the water in the fountain. 

Johnny, being scared from the first time he got jumped and worried that they are going to kill Pony, kills him by stabbing him.

We are not supplied with that much information about Bob in this excellent novel. However we are told that he is handsome, wealthy, and most importantly, a Soc. He is Cherry's boyfriend, and it is clear that he likes to drink, but that this causes problems in his relationship with Cherry. Note what she says to him in Chapter 3:

"Bob, I told you, I'm never going out with you while you're drinking, and I mean it. Too many things could happen while your're drunk.. It's me or the booze."

However, it is also strongly indicated that it was Bob and his gang that was responsible for Johnny's attack that has left him so traumatised. Note what Ponyboy sees as the car pulls up:

Johnny was breathing heavily and I noticed he was staring at the Soc's hand. He was wearing three heavy rings. I looked quickly at Johnny, an idea dawning on me. I remembered that it was a blue Mustang that had pulled up beside the vacant lot and that Johnny's face had been cut up by someone wearing rings...

So, clearly Bob has a violent side to him that, when unleashed, could be incredibly destructive. However, as Cherry tells Ponyboy later on, it would be wrong to label him as a violent psychopath alone:

"You only knew his bad side. He could be sweet sometimes, and friendly... Bob was something special. He wasn't just any boy. He had something that made people follow him, something that marked him different, maybe a little better, than the crowd."

It is important that the author presents Bob as just human like everyone else in the play. He is another character that would benefit from looking at sunsets, and another young man caught up in a system beyond his understanding and control. So whilst we are perhaps tempted to think of Bob in purely negative terms, it is important to maintain a balanced view of his character.

One of the challenges he faces is the fact that his parents are dead and his oldest brother is supporting the family. They struggle to make ends meet and Pony knows this. He also feels the weight of the class separation between he and his "greaser" friends and family and the "socs," the kids with the money and the connections. He sees the kids around him who get into trouble with the law, treat school like a joke, and even those like Darry who have everything they need to succeed but didn't have the money to take advantage of this hard work and talents.

Pony also faces the challenges that arise because he is with Johnny when he kills Bob and then sees Johnny do something heroic and end up dying. He worries about whether he will get in trouble for Bob's death and also struggles with seeing people close to him like Johnny and Dally die. It is difficult for him to see a way out of these troubles when it seems like everyone he knows ends up in the same boat.

The challenges that Bob Sheldon faces in The Outsiders include peer pressure, insecurity, excessive alcohol consumption, and violence. Because Bob comes from a well-to-do family, he does not face the same financial pressures that affect many of the characters. Bob’s privileges support his position within the Soc gang, but that status brings its own set of expectations to conform to his peers and even take a leadership role among them. Bob’s sense of personal insecurity—especially in regard to his relationship with his girlfriend—goes hand in hand with his tendency to drink too much alcohol. In turn, the peer pressure and the effects of the drinking combine to his rationalizing his involvement in violent behavior.

Bob’s status strongly influences his negative attitudes toward the greasers, and he feels justified in attacking them. His animosity toward Ponyboy, which stems in part from Pony’s association with Johnny, escalates when he finds Pony talking with Cherry, his girlfriend. His problems become factors in his death, as Johnny kills him for attacking Pony.

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."