Sweet, sunny Martin first came to notice singing “My Heart Belongs to Daddy” in 1938. Five years later, she was headlining Kurt Weill and Ogden Nash’s “One Touch of Venus.” But it took two Rodgers and Hammerstein shows to cement her fame: “South Pacific” (1949), a musical that showed she could act as well as sing, and “The Sound of Music” (1959), in which her wholesome presence was essential. In between came her spirited portrayals of Peter Pan, onstage and in two television versions. Martin remained beloved by the public until her death, but after “I Do! I Do!” (1966), she seldom appeared on the stage.