I'm not sure I'd call it a must-see, but I really like Out of This World (1945) in which Diana Lynn leads an all-girl band with guy singer Eddie Bracken (dubbed by Bing Crosby).
For the 1950's, you've got to add one of my favorites, definitely a must-see, L'i Abner (1959). It's dated and not dated at the same time, being such a perfect time capsule of 50's social and political satire, with a truly witty and inventive score.
Also Pajama Game, which was discussed in another thread here.
For the 1960's, definitely Gypsy. It may not be the definitive cast, but it's one of the all-time great musicals.