Which even gives out why he is so motivated by vengeance. Here is a summary of the plot - Kratos was a Spartan general fighting in some barbarians (or something) but they manage to take him down and when it seems like the battle is lost, Kratos prays to Ares, the god of war, promising him anything to not let this be the end. Ares actually hears his plea and decides to grant him his wish, if Kratos agrees to serve as Ares' personal warlord. Faced with a choice between death and something like a deal with the devil, Kratos gladly takes up Ares' offer. The battle is not lost and now Kratos serves Ares - blindly following all of his orders which are about waging war, death and destruction. Kratos even revels in it as he becomes an extention of Ares' will. One day, he is ordered to destroy the temple of one of the other deities (I think it was Atina) - Kratos does so slaughtering everybody who comes in his way not caring, not even seeing who they are - women and children included - empowered by Ares and the almost battle trance he has been steadily developing following the god's commands.
Two figures in particular we should not here - a defenceless mother and her daughter who had hidden in the temple from the battle outside and whose blood Kratos spilled as readily as taht of any soldier. Those were his own wife and child. Ares tricked him into killing them, to shape him into the most ruthless instrument of war. As the temple burns down, and Kratos realises the horrific truth, priestess the of the temple (who I think was Atina herself) curses him to carry the shame of this day for an eternity.
His skin is not originally pale white. These are actually the ashes of Kratos' own family forever bonded with him to always remind him of what he had lost.
It is no surprise then he feels so bitter and hates Ares so much, spending the entire first game on a quest to end him.
In fact, I must say, the first game had a really, really good ending. The final battle against Ares is grand - there is a physical confrontation when they whack each other with weapons, sure, but the true beauty comes in a later stage of the battle which is inside Kratos' mind. In there, Kratos sees his wife and child again, both cowering in a temple, while many copies of Kratos come and try to kill them. You, the real Kratos try to defend your family from your worst fear - yourself. Not only that but the battle takes its toll and the landscape starts dissolving around you leaving Kratos with less and less choice and freedom, just like his servitude under Ares did when his life was devoted to just that fighting. And the most powerful part in that battle, I think, while you have to protect your family from being killed, it's not a simple "HP bar runs out - you lose" thing, you can heal them by stopping the violence to...lovingly embrace the two.
Notice how Kratos is literally giving his live for them - the health restored to them is taken from
his health bar.