To answer your question, there are so many areas to look at to determine who was greatest. we need look at all kinds of areas such as land mass, population, military, leadership, government structure, wealth, foreign relations, and last I'll list comparison to other nations in time period. Feel free to name others. knit the parts all together.
As for my answer, I would have to say the Romans' republic and empire developed the best overall nation based on their time period. Excellent size in land mass and eventually after the fall of...well... everyone else, Rome had great control of the Mediterranean for transportation and trade. like most any nation, the politics changed but it sure was able to govern well in territories not just as a massive empire. Uprising happened but Rome's military and government knew how to deal with it. What is wonderful is that Rome was a nation with a long history.
Now to deal the bias of the positives, here are some things that didnt make Rome so great. Corruption, extravagant spending, civil wars, serial regicide, military upkeep costs, and wars that ended badly for Rome.
Here are some competitors on my list in the time era (no particular order)
Alexander's Empire + Diadochi era
China (Qin and Han dynasties)
Sassanids (226-651)
Mauryan Empire c340 BC- 181BC