Love musicals and love the history of this movie genre and how it changed, evolved, died and returned several times. It's a genre that can not go away for too long cause there's always a hit bio or a new music craze that can be used for a successful movie.
You all mentioned most of the best known periods/studio eras of musicals. Of course M-G-M ones are my favorites, it is the studio that capitalized the most on this genre and built it into a pure art form, reaching some of the peaks that are hard to be repeated. By the mid 50s, as the Metro musicals started to fade out, it was these grand
Rodgers and Hammerstein adaptations, mostly done at Fox, that took over and ruled the box office into the mid 60s. Out of all of these, I only really love The Sound of Music (1965) and Oklahoma! (1955). Everything else I find to be overlong, boring at times and the songs don't do much for me either, to be honest.
Going back in time, I also love the early
Warner Pre-code musicals, mostly done by Busby Berkeley. 42nd Street (1933), Footlight Parade (1933), Gold Diggers of 1933 (1933), Dames (1934), etc were all so much fun and exciting, just like most movies done in this period. Berkeley's mind-spinning choreographies and dance numbers art still unmatched. There's a lot of realism in these movies, the characters are people struggling in the show biz during Depression era, just like in any other Warner movie of that time. The casts are also great, I love Ruby Keeler and her clumsy dancing, Dick Powell, Joan Blondell, Ginger Rogers, James Cagney etc. If you haven't checked these out, be sure to do it, you'll have a blast.
At the same time, the refined Astair/Rogers musicals developed over at RKO and I still haven't seen any of these. Somehow I don't feel much excitement about doing it either.
Back to MGM, their true golden age of musicals started in the early 40s, with the formation of Arthur Freed unit. Of course they made many musicals during the 30s as well, developing many stars like the amazing Eleanor Powell and her step dancing, the aforementioned Jeannette Macdonald and Nelson Eddy series of movies which I can't get into, sorry but these operettas LB Mayer loved so much are not my thing. They continued this tradition with Kathryn Grayson and Jane Powell to a lesser extent. During the 30s, it was also interesting to see many of their dramatic stars appear in musicals, having to sing, dance or perform, usually with embarrassing results.

No one was spared, Stewart, Crawford, even Gable had to do a dance or two.
From Metro-s golden period, I love
Kiss Me Kate (1953) with Kathryn Grayson, Howard Keel and the fab Ann Miller. Grayson's operatic singing is actually fitting here and she does a fine job with a juicy role. She was paired with Keel several time successfully. But it's Annie who spins the dancefloor and steals the show, as usual.
I also love
It's Always Fair Weather (1955), a lesser known and a very different Gene Kelly musical with a pessimistic, sarcastic tone, somehow fitting since it came at the end of the studio's golden age of musicals. Cyd Charisse has a marvelous dancing scene in the boxing ring/gym.
Dolores Grey is also great in this, she appeared in a few MGM movies in the mid 50s and always left an impression on me.
I also enjoy some truly lesser known MGM musicals, oddities like
Athena (1954) that are just a lot of fun. This one includes a bunch of bodybuilders parading their goods around, the goody two-shoe Debbie Reynolds, operetta singing Jane Powell and Louis Calhern residing over a family of new age, Greek mythology gym freaks. Yes, it has to be seen to be believed.
As I type this, a Nelson Eddy, sans Jeannette Macdonald, movie called The Chocolate Soldier (1941) starts on TCM. A woman called Risë Stevens is his partner, operetting in this one. Maybe I'll give it a look....