I know this is supposed to be simplified, but there were more religions than this. You should add other forms of religion to the basics.
For example, christianity before this point was divided into Eastern Orthodoxy, the Catholic Church, and various heretical cults, the most notable of which is Arianism.
You should start with Paganism, and choose between Polytheism, Monotheism, and Philosophy.
Polytheism religions should include: Egyptian, Hellenic, Hinduism, and Shinto
Monotheistic religions should include: Christianity, Judaism, and Islam.
Philosophies include: Confucianism and Buddhism
Christianity should be divided into Catholocism, Eastern Orthodox, and Heretic.
Judaism is fine the way it is.
Islam should be divided into Sunni and Shi'ite
I'd have random benefits to the religions as well. Perhaps the Christian techs lower build time, but has an IC penalty, and Islam ups experience in values, but increases partisan levels.
There should be different benefits and disadvantages for the player to choos a religion.