Let’s get on with it (from #1 most must-have to #10 least must-have, with Wiki and forum sources):
1. Ottoman Empire / Turks
World’s most powerful Empire lategame (Turks have several large empires in AoE4, Ottomans are the successor of Seljuk Empire), very long-lasting in history, extrmely unique, deep, asymmetric, game-changing as an AoE civ. The Turkish concepts of hybrid nomad-to-settled civ, mathematical asymmetry of weak economy but stronger military units in same proportion, trade interference, battle veterancy, boost troops with a different army band song for each situation could transform Age of Empires. The Ottoman Empire defeated the most major world civs among all civs, fought major powers on 3 continents simultaneously, destroyed the Byzantine Empire and ended the Middle Ages, had 80-90% historical win record against French, English and HRE, besieged HRE capital Vienna twice, defeated many European countries together in Manzikert, Nicopolis, Varna, Preveze etc, destroyed the Bulgarian Empire, the Mamluk Sultanate (which had defeated Mongols 4 out of 5 battles), the Ethiopian Empire, the last Timurids (which disappeared Mongols from history) and the “Fortress of Europe” Hungary. The Ottoman Empire was first and only to use Great Bombards extensively in siege. Matchlock musket is the most important military innovation that ushered in the modern world. Colossal architecture and wonders. The Ottoman Empire was the Earth’s 3rd most populous empire in 1600 after Ming and Mughal India (HRE not a single state), and number 1 in military power. Amazingly, the Ottoman Empire remained a world power until World War I in the 20th century.
2. Persia
The most ancient large, unified Empire in the history of the world, centuries before Han China; Persia is a millenia-old giant of human civilization and an extremely unique, asymmetrical candidate to AoE4 faction. Colossal literary achievements like the Shahnameh (The Book of Kings) tower over much of the world. Absolute supreme architectural sophistication unmatched anywhere deeply, pervasively influenced all of Central Asia, Indian subcontinent, the Middle East, Southeast Asia; the “soft power” of Persia spread further than any other civ on Earth, and this could be game-revolutionary for AoE. In the early centuries of the Middle Ages, dominant Persia had several classical superpower wars against the Byzantine Empire. At the end of AoE4 time, Safavid Persia was again a true world power with massive population, formidable advanced military, and proved the Ottoman Empire’s most challenging foe in many massive wars. Habsburgs/ HRE seriously depended on ally Persia to slow down the Ottoman Empire’s advance into the heart of Europe. The mechanism of “appeal”, probabilistic conversion power by “Masterpieces” (architectural landmarks, literary works) of increasing conversion radius based on “Soft Power Level” (similar to Rus bounty level), could really revolutionize Age of Empires.
3. Byzantine Empire
Longest continuous Empire in history, the cosmopolitan and sophisticated Byzantines are the one and only genuine heir to the Roman Empire. A beacon of light and hope of civilization among the brutal Dark Ages, advanced Byzantine armies criss-crossed Europe and Asia defeating numerous barbarian nations for centuries. Classical superpower rival to Persia and later, more importantly, to the Turks / Ottoman Empire. The titanic, iconic clashes between Byzantines and Ottomans held the attention of the world and defined an era.
4. Mali Empire
By far the largest African empire with hyper-cool and unique architecture of colossal mud palaces and wonders, “Sahara Empire” Mali was the world’s 3rd most populous empire in 1500 (almost 20 million inhabitants) and kings of long-distance trade. Emperor Mansa Musa was the richest man who ever lived.
5. Inca
With 12 million inhabitants in 1500, the super unique, faraway Inca Empire was actually twice as large as the Aztecs then, by far the largest empire in the New World. Fascinating Macchu Picchu is a universal wonder of humankind.
6. Indians / Vijayanagara
India is a timeless civilization; it accounts for 1/5 of humankind nowadays and had many important states in history. Vijayanagara Empire was the most important winner state in South India lategame in AoE4, as well as 4th most populous empire in the world in 1500.
7. Japan
Semi-isolated Japan was basically never an empire during AoE4 time and was often not even a unified country. But the archipelago did hold a large population for centuries and is very hyped and popular in Western mainstream media and entertainment, earning a spot as a marketable civ that could perhaps boost AoE sales. Joseon / Korea is relatively less unique than Japan, therefore less valuable as a candidate civ.
8. Spain / Iberian Union
Spain became a colonial superpower in the New World lategame, interacting much with Inca and Aztecs; perhaps significant naval power Portugal could join an “Iberian Union” civ with Spain. Not highly unique compared to other Western Europe civs though.
9. Ethiopia
I feel Africa deserves two civilizations and Ethiopia is a deep, proud, fascinating ancient civilization and multiethnic empire with unique writing system, government and traditions.
10. Hungary / Italian States (equal-rank alternatives)
Sturdy, legendary strong-army Hungary defeated the Mongols alone and was the medieval “Fortress of Europe” for centuries until its total destruction by the Ottoman Empire in 1526. Wealthy Italian states Naples, Venice, Florence and Genoa could combine together to form a rich and interesting civilization (HRE was not a single country either).