There are lots of conflicts in these chapters -- Holden against just about everyone he ever meets, essentially. But it all boils down to two conflicts that continue through the whole book. The two conflicts are Holden vs. society as a whole and Holden against himself.
We can see Holden in conflict with what society expects from him most clearly in Chapters 1 and 2. We see this from the fact that he has been thrown out of Pencey and we see it in the way that he interacts with Mr. Spencer. We also see him in conflict with Ackley and Stradlater.
A lot of this is because he is not sure what or who he wants to be. We can see this partly in how he has the red hat. He pretends to not care what society thinks of him, but there are times when he won't wear the hat so as not to stick out too much.