Hmmmmm. I'm going to throw some ideas out off the top of my head. What follows is in no way a carefully considered thesis of any sort!
- I would assume that in a post-apocalyptic world, a religion, a faith of sorts, would be even more necessary than usual. Life - survival - would be much more difficult than it is for us now. Someone above mentioned the need for societal structure and hope. I agree.
- Not sure I would do much very different than major Judeo Christian religion(s) do it. I'd keep the 10 commandments and add another, supreme commandment, which would be the golden rule, do unto others...
- I would incorporate elements of paganism, given that life will probably be a lot less technologically sophisticated than it is now, we would probably be back to subsistence living, at least for awhile, and I think paganism would comfort people, perhaps give them some sense of hope or control over their own destiny, which would now be more intimately tied to the earth, seasons etc., than it is for westerners these days.
- assuming I am the head of the religion, I would not permit a state/government separate from that religion, not for the first while anyway. This new society would not be a democracy, again, not at first. It would be more of a benevolent religious dictatorship
- my religion would emphasize the value of private property and the sovereignty of one's person/body. Crimes of violence would be punished harshly, non-violent crimes less so. A prison system would be one of the first institutions to be formed, as would a court system based on what we have in the west today - common law, jury of your peers etc.
- rituals and festivals would be emphasized and played up. I believe these things are beneficial, especially to a pre-modern society, they allow people to feel community, to bond, to let off steam and so on
- the final word would be mine - I would be a pope of some sort, but decisions would be team based, and I would handpick my team aiming specifically for people with different ways of thinking and/or communicating than mine, and a variety of different kinds of 'intelligence'.
- the need, in the beginning, for strong arm tactics seems fairly clear to me, and I would build and employ an army of men who answered to me to do this job for me/my team. Loyalty would be the one main quality I looked for in them.
- I believe religion is in many ways the opiate of the people, but I differ from some in that I basically believe the opiate is generally necessary to provide hope and relief from the harshness and reality of life
- after basic survival needs were being met for most people, would come the time to develop higher levels of society/government and make more complex decisions about ruling/rules/laws etc. I.e. refinement would come later, when most people were fed, housed and basically safe from serious crime, which could obviously take awhile.
Anyway, some of my initial thoughts. I'd crib a lot from Christianity, obv.