As a Pharisee of the Pharisees, what did Saul believe?

Well I guess it would start with the idea that God was the God of very Gods - he had no rival. Sure, the other nations may have their "gods," but none could compare to the God of Israel. He, and He alone, had created this world, protected his people through Egyptian captivity, led them under Moses to the promised land, and spoken through the prophets during times of great darkness. And now, even though they were living in Roman-occupied lands, they were able to worship God pretty much as they pleased. So, if they kept Rome happy, they were happy.