The original Kratos was basically one big long revenge story. Almost all of it justified and satisfying, but basically wiping out the Greek Pantheon was his ultimate goal.
His actions were reckless and fury driven, but often went over the top, both in violence and in actions.
My favourite example is from GoW: Ragnarok, when certain characters are reflecting on Kratos’ past, and how the one story of him killing the Sisters of Fate must truly be myth, then he corrects them saying it was true and how they deserved it. The third character then shines a present light on the fact that he did that in the past and says, “that’s the most dangerous and irresponsible thing I’ve ever heard.”