By coincidence, a while back I became fascinated by Roman religion. Roman religion is so much more complex and multifaceted than just the pantheon of gods and Greek-derived myths we learn about in school. It infused every aspect of society, including tutelary deities, ancestor cults, family cults, demons, spirits, festivals, sacrifices, etc. Every person was thought to have their own spirit, called a genius, which is where we get that word (it also influenced His Dark Materials)

For priests specifically, Wikipedia has a very good page on it: https://en.wikipedia.org/wiki/Religion_in_ancient_Rome#Public_priesthoods_and_religious_law

See also: http://www.classicsunveiled.com/romel/html/religion.html

I became interested in this topic after reading The Ancient City by Foustel de Coulanges. I would recommend that book if you want to know more.