Considering the limitations that I have on my own time dear (with A-levels teaching in the morning to do and just and evenings spared for prep), I can only briefly touch upon the two empires here:

Sassanian empire: Focus on the administrative system (which was adopted readily by the Abbasids later on), the refined level of arts and culture and the military might of the Persian arms.
However, remember that by the time Islam emerged onto the world stage, the Persians were reeling from a host of problems which included dynastic troubles, perpetual war with the Byzantines and a general decline in the financial security of the empire.

For Babylon, just read up on Hamurrabbi, his edict on universal rights and the glory of the Assyrian empire (centered on the city of Sumer) and Akkadian empire (centered on Akkad). At most, only MCQs can come from here.

Byzantines, as I have stated earlier, are comprehensively covered by Hitti and Ameer Ali.
Jazakallah khair