In some reading I was doing, it was said that most Broadway...scholars(?) will agree that the 4 greatest shows are West Side Story, Gypsy, My Fair Lady, and Fiddler, with I guess Sweeney knocking on the door. So good picks, IMO.
Oklahoma! is without a doubt one of the most important and influential shows but I think when you compare the quality with the other 4, you can't really put it up there, IMO.
"If there was a Mount Rushmore for Broadway scores, "West Side Story" would be front and center. It snaps, it crackles it pops! It surges with a roar, its energy and sheer life undiminished by the years" - NYPost reviewer Elisabeth Vincentelli