I'm starting God of War 2 - not sure if I should play the Greek trilogy before jumping into the Norse games or not, but I figure more context couldn't hurt.

From the opening cutscene alone, Kratos is kind of an idiot.

Athena: Kratos, you're angering all of Olympus with your senseless war-mongering.
Kratos: I don't care.
A minute later, Kratos enters the battlefield to wage war directly and is struck by lightning.
Kratos: WHAT? HOW DARE YOU BETRAY ME?!

"Drain your godly powers into this sword, Kratos, and you will reach your full potential."
"What I do now, I do for the good of all Olympus."
What could possibly go wrong?

I don't remember it being mentioned in the first game that Kratos is Zeus's son, but it seems like Zeus was afraid of Kratos killing him and taking his place, even though Kratos seemingly had no intention of doing that. (And this will probably motivate him to do that)

It's a small touch, but I like how the save points switch from saying "Zeus has given you the opportunity" to "Gaia has given you the opportunity" after the opening.

Kratos is stabbed to death by Zeus, and upon being resurrected and being sent a pegasus, his first words are basically "TAKE ME TO OLYMPUS SO I CAN FIGHT ZEUS!"