How 'greatest' is defined will definitely bias the potential pools of military leaders. Are they those that won the most battles, most significant battles, conquered more land, was successful but had only minimal losses, or what?
I would argue that the greatest overall was Shaka (sp?) Zulu. Using comparative primitive weapons (metal tipped spears, hide shields, clubs, etc.), he managed to conquer much of Africa and did so on foot, not with vehicles or riding on animals. In fact, the Zulu empire was able to stave off the much better armed British Empire for many years and they did have beasts of burden, vehicles (wagons pulled by beasts), etc.
Shaka had what has to be one of the most shrewd battle strategies of any military leader and his strategies were brilliant. After attacking an opposing village or group, Shaka gave the losers a choice. They could all be killed or agree to join Shaka. Most joined. So he was able to conquer a place and then make allies of the inhabitants. In doing so, his army grew as did the population of his empire. The evergrowing army needed more and more supplies. These were supplied by the non-warriors of the villages conquered and made allies.
Something funny about his strategy was just how well it worked. As his ranks grew, so did his reputation. Upon coming upon a village that was to be attacked, in several cases the villagers knew he was coming and when they say his giant forces, surrendered without a fight and joined him.
So, Shaka was able to conquer a large area of Africa, dramatically increase his power, defeat enemies, make allies of enemies, and hold off militarily superior forces with nothing better than iron and stone age technology. As with all empires, one of the biggest limiting factors of controlling a large empire was how well information was transmitted and received. Like the Inca, Shaka relied on message runners. As the empire got larger, the ability to move information via message runners took longer and longer until which time the information was too old to be useful. Also, without written language, the messages had to be short enough to be able to be learned, remembered, and then transmitted to the next runner in the sequence such that the runners would not confuse, add to, or delete attributes of the message.