I’ll go first.
First: Inca and either the Maya or the Aztecs
Second: Ottomans and Byzantines
Third: Persians and Indians
Fourth: Japanese and Mali
These four would do a good job of highlighting almost all of the largest empires during our era. Obviously limiting it to 16 civs will leave several big names off the list. But this list would allow for some really cool diversity in civ and unit design to bring out cool gameplay and still keep the civs grounded in a list of mighty empires.
Obviously reasonable minds can disagree. That is why this forum exists.