Since I'm so damned old, and have been going to theatre since the late 1950s (got to see Merman in HAPPY HUNTING, GYPSY, ANNIE GET YOUR GUN and DOLLY), my picks are a bit different (although I love reading the lists):
1. ANYONE CAN WHISTLE with Lee Remick and Angela Lansbury (I had tickets, could only go to Saturday matinees, and the show closed before my May matinee came up, never got over it, and convinced Steve and Arthur to let us do an off-Broadway revival in 1992 as a three-week benefit for BroadwayCares/EquityFightsAIDS).
2. THE MUSIC MAN with Robert Preston and Barbara Cook
3. CAMELOT with Richard Burton and Julie Andrews (saw it near the end of its run, with William Squire, a Welshman like Burton, giving a wonderful carbon copy of Burton, and aging soprano Kathryn Grayson doing unnecessary runs and trills).