What kind of copyright should I apply, and where to apply it?

You write to the publisher.

How much are you using? There are exceptions to copyright for “Fair Use”.

@zenvelo. Thank you for your answer, I am writing a music lesson book, so I guess it’s convenient for students if I include whole sheet music in the book. What is “Fair Use”?

Fair Use is an invention in US Copyright law that lets you quote small sections of a copyrighted work for criticism or interpretation. It doesn’t allow for large sections, like complete compositions, to be copied and used.

For sheet music of musicals, you need to see who the publisher is (it should be on the sheet music) and apply to them. So will let you copy it at no cost; most will want to charge some sort of payment. Some will not give you permission at all.