I vote for three in depth, because (1) in-depth allows you to present what's interesting about each one, while overviews are often too shallow by necessity to show what's really cool about the discipline and the subject; (2) I personally have always hated having to write papers with a passion for which I have no adequate words; and (3) doing in-depth looks gives you room to present the various analytical tools like Marxism in context, and with immediate illustrations of how they work in practice.

If I had a choice, I'd also vote for the civilizations being one American, one East Asian, and one West Asian/Northern African, but that's just me. I do realize you probably have no alternative to covering Egypt, even if Indus/Harappan might be more interesting.