Your instructor usually determines which style you must use in your papers. If you don't know--ASK!
Generally, you will only use one of these style manuals as a guide for how to cite sources and arrange parts of research papers. However, you may find general advice on research in all of these.
MLA Handbook by 
A Manual for Writers of Research Papers, Theses, and Dissertations by 
Publication Manual of the American Psychological Association by Books on writing about music are at ML 3797.
A Style and Usage Guide to Writing about Music by
In A Style and Usage Guide to Writing About Music, Thomas Donahue presents a collection of guidelines to help express through the written word the special notations, terms, and concepts found in the discipline of music. It concentrates on questions of style and format in the interest of good formal writing within the context of United-States English, so that writers may communicate their ideas clearly and effectively.While compiling the guidelines, Donahue reviewed content from many other music and general guides. He documented the most common formats in order to assist the writer in selecting an appropriate format for the given circumstance when more than one may apply. The book draws on profuse musically-oriented examples and is arranged by topics both musical and typographic, such as the proper use and spelling of composer names and musical concepts; the use of notes, pitches, and octave delineations; letters and numbers employed to describe form and harmony; when, where, and how to apply compound words and hyphenation of terms and names; and the proper citation of musical and audiovisual sources. The book concludes with a glossary of typographic terms, a bibliography, and a comprehensive index, making this a valuable resource for students, scholars, teachers, and writers.
Music in Words by
A textbook and reference book "about the way we research music and write about it." Graduate student level.
A Handbook for Preparing Graduate Papers in Music by Quick Citation Formatting in Databases.