I voted Imperial Rome as well. If I recall correctly, during the rule of Augustus Caesar (Octavian, who presided over much of the Pox Romana), Rome's
standing army consisted of around half a million well armed and extremely well trained troops with loyalties to Rome's Caesar, not just the Generals and Prefects.
In
those days, having
absolute and immediate control over more than half a million, battle-ready legionnaires was inconceivable to most, as would 50 million or so US GIs be inconceivable to most of us today. What
is our military personnel count today, around two million?
Imagining the current U.S. military over 25 times greater in size than it is today gives me a headache.
Rome's legions were an incredibly mobile military machine that outclassed anything of its day, bar none. Capable of amassing incredible numbers of legionnaire across its vast empire in impressive time (due to the construction and utilization of waystations and roads) and practicing awe-inspiring military discipline, the Roman war juggernaut seemed all but invincible.
But that too, did pass.
I've heard ancient Greece being considered the fountainhead of modern civilization, and that may be true... but when it comes to military power, that collection of Greek
city states had nothing on Imperial Rome! The Greeks only "pulled it together" during the Persian war... after that, it was each Greek city-state for itself (as the Athens/Sparta Peloponnisian war illustrated quite nicely)
So, if the question is the "most effective during their existence in history"... I'd put my money squarely on ancient Rome without hesitation. But then, I thought that would be obvious to most.