The first two styles are known as “in-text” citation styles, which means that you give some information about the source directly after the quotation, but leave the rest to a list of References (APA) or Works Cited (MLA) at the end of the paper.
You should check with your instructors about the style they want you to use.
When in doubt, remember that the goal of your citations is to help a reader who wishes to consult your sources directly.
When developing a historical explanation from multiple primary sources, using footnotes instead of inserting parenthetical information allows the reader to focus on the evidence instead of being distracted by the publication information about that evidence.
The footnotes can be consulted if someone wants to track down your source for further research.