Igor Markov's answer to Why does the US government spend so much on military? Jon Davis' answer to Given that China is fine without blue-water navy, why does the US need one? Being even is the Deadliest form of Warfare
Imho the most influential war in history is the Caesar Augustus' failing attempt to conquer the Germans. He sent two legions over the Limes Renano expecting to tame the german population. It didn't happened: in the Battle of Teutoburg Forest the army of 15.000 well trained roman solders was completely slayed but Germans. In a what if...
What made the battle important was that it was the first large  battle of the war, and, in fact, involved more soldiers than any  other battle of the war.