If Tacoma Little Theatre's history page is correct, the first live musical I would have seen was IRENE, although I have no memory of that show.  The next four years I do remember:  CAROUSEL, THE DESERT SONG, THE RED MILL, and OKLAHOMA.  The next five years I saw:  SOUTH PACIFIC, BRIGADOON, SHOW BOAT, ANNIE GET YOUR GUN, and ANYTHING GOES.  Somewhere in there I also saw ONCE UPON A MATTRESS with Imogene Coca, King Donovan, and Edward Everett Horton.  The first Broadway production  was the all-black cast of HELLO, DOLLY! starring Pearl Bailey and Cab Calloway in 1969.