Yes I read them in the order presented. The order kind of makes sense (sem 1 & 2: Ancient Greece, sem 3: Early christianity/rome, sem 4: renaissance, sem5/6: enlightenment, rise of democracy, sem 7/8: early modern period.) By the time you get to Shakespeare there are echoes of stories you have already read.
In terms of a strategy for retention, I kept a small book of quotes from the works and would add to them weekly (no idea where this is now).
I should say that the latter stages of the course has large sections that are for essay writing and projects. I skipped all this but added other books instead. These were mainly American literature (Twain, Fitzgerald, steinbeck), English literature (Bronte, Dickens, Orwell) and some older stuff (Suetonius, Xenophon).