How did the Greeks/Romans think about War and Peace?

This can't really be answered well until you clarify what time period and specific people you mean. Are you talking about before the Greco-Persian wars, which lasted from 499 BCE to 449 BCE? Do you mean during those wars? Or do you mean when Rome conquered Greece after defeating the Corinthians in 146 BCE? Or do you mean when the Western Roman Empire fell (which I date to 476 CE) and left Constantinople as the remaining Roman Empire, called the Byzantine Empire, a time in which the line between "Roman" and "Greek" arguably blurred into nothing?

Then there is the issue of using the term "Greeks." "Greeks" are historically a diverse people, not really forming a single "Greek" identity until forced to fight together against the Achaemenid Empire, after which the lines of division by dialect, geography, and political systems threw them into a series of wars. The Spartans, Athenians, and Corinthians are all "Greeks" but their views on war differed greatly from one another, and these views changed drastically over the hundreds of years of their existence.

So to clarify, what time are you asking about specifically, and could you be more specific about what Greek people? Also what /u/pathein_mathein asked about "traditional/mythical," what do you mean by this?