If you are free to choose a citation style, use one you feel comfortable with, and use it consistently and correctly for the entire assignment.
Many of the resources on this page are style manuals - they provide information on all aspects of formatting papers in a particular style. These manuals usually have 1 or 2 chapters on how to cite sources.
APA is used in the social sciences. It is also commonly used in business and education.
AMA is used in medical and health fields (with the exception of pyschology).
MLA is used in the humanities.
ACS Style is used in Chemistry.
Chicago is used in the humanities, especially History. (If you have been told to use Turabian style for citations, it is almost identical to Chicago.)
IEEE is used in Engineering.