When you are making decisions about how to integrate quotations into your essay, you might imagine that you are reading the essay out loud to an audience. You would not read the parenthetical note. Without some sort of introduction, your audience would not even know that the statement about Roman antiquity was a quotation, let alone where the quotation came from.
The principle doesn’t change. In American English, use double quotes for the outside quote and single quotes for the inside quote. In British English, do the opposite. Let’s say you need to quote a book for an essay, and the passage you have in mind contains a quote from some other source. Imagine the original passage from the book looks.