There's only one right way to coninue this series and it's very plausible a terribly easy to do.
There is a character in GoW(and also obviously in Greek mythos) who has served multiple important roles through out the games, but has had no actually appearances or direct mentions. He has been shown to have only been force for good so far, and was not one of the gods corrupted by the opening of Pandora's box.
Apollo.
Kratos has benefited from Apollo's exploits in multiple ways, even to the point of using Apollo's legendary bow in GoWIII. Even in Ascension Kratos had to go through two tributes to Apollo in order to complete his quest(one the temple of Delphi, home of a powerful oracle, and the other a titanic statue of Apollo). He's made appearances in various art throughout the game as well. He depicted in many different ways in this art, so how he looks or looked at any given time is uncertain to us.
What i'm getting at is a prequel, before the time of Kratos, about the god Apollo. The way Greek Mythology, at least in the GoW series works, thousands of years are like nothing to most beings, so you could have prequel a thousand(or at the very least a few hundreds) years before the first chronological Kratos venture and not have to worry about changing too much.
There are plenty of Greek/Roman mythological beings and beasts never seen or mentioned(or killed), and we would get a protagonist with emotions other than pissed off, pissed off and sad, and really pissed off(I actually like Kratos being like this, but still).
He definitely has a power set that can lead to fun gameplay, as he is a/the god of: light and the sun, truth and prophecy, archery, healing, plague, music, poetry, and some other things. He is a god of light and the sun, but Helios is shown to be that in GoWIII, and we know gods can be replaced, as Kratos did to Ares, but how did this come to be for Apollo?
What became of Apollo and why were his legacy and the things he left behind left in the way they were? We don't know, but we could easily find out.
