What should be underlined or quoted in this sentence?

The Dance of the Sugarplum Fairy is a melody in The Nutcracker Suite.

The nutcracker suite underlined? What about famous dances?

Yes, The Nutcracker Suite is Underlined. Music is in quotation marks.

A case can be made to italicize or underline "The Nutcracker Suite," but music and works of music are not usually italicized or underlined, they are within quotation marks.

"Use italics (underlining) to indicate the titles of books, magazines, newspapers, paintings, and the names of ships, airplanes, and man-made satellites." -- Walsh (1966)

To be more complete, both "The Dance of the Sugar Plum Fairy" and "The Nutcracker Suite" are works of music, the difference being that the dance is contained in the larger work. (And the suite is excerpted from the even larger work, "The Nutcracker" ballet.)

In this sentence, the title "The Nutcracker Suite" should be either underlined or italicized, as it is the name of a specific musical composition. However, the specific names of famous dances do not need to be underlined or quoted unless they are part of a larger work or composition. In this sentence, "The Dance of the Sugarplum Fairy" is a famous dance within "The Nutcracker Suite," so it does not need any special formatting.