In the special feature on Netflix where they're all at a restaurant talking about their careers, Pesci says he was willing to play Tony Pro, but that Scorsese insisted on him playing a boss this time.

I noticed Scorsese likes to use early rock and roll ballads as opposed to the classical "Rat Pack" pop most mobsters were probably listening to in the 1950s. The music Scorsese uses in this period is typically what teenagers listened to. Makes sense considering he was one at this time. This could have something to do with frequent collaborator Robbie Robertson (of The Band), too, who was music producer in this and many of Scorsese's other films.