Founder Beliefs:
5 - Ceremonial Burial: +1 Happiness for each City following Religion
4 - Church Property: +2 Gold for each City following Religion
4 - Initiation Rites: +100 Gold when each City first converts to this Religion
3 - Interfaith Dialogue: Gain Science when a Missionary spreads this religion to cities of other religions
3 - Papal Primacy: +15 to Influence resting point with City-States following this religion
1 - Peace Loving: +1 Happiness for every 5 followers of this religion in non-enemy foreign cities
1 - Pilgrimage: +1 Faith for each foreign city following this religion
5 - Tithe: +1 Gold for every 4 followers of this religion
3 - World Church: +1 Culture for every 5 followers of this religion in other civilizations
Ceremonial Burial is obviously good for ICS type strategies and any wide empire really. If you intend to spread your religon this should always be a good belief.
Church Property is a good gold generating belief. Better if going wide and even better on standard size plus maps. However, if your neighbor's cities can't be flipped it will become redundant in comparison to Tithe.
Initiation Rites is clearly very powerful early game, where it can give even 10 turns worth of gpt in a moment. You get 50 turns worth of Church Property in a single turn and you do not need to hold onto the city. But it is a one-time thing.
I have never used Interfaith Dialogue and I am unsure of how much science it gives exactly, so I gave it a middle rating. If you get something like the Mosque of Djenne then it seems potent.
I've never used Papal Primacy, but it seems powerful when using Greece with that Patronage Policy plus pledge to protect but if not, it does not look apealling.
As far as Peace Loving goes, it seems as though Ceremonial Burial will be better in almost all cases. If your trying to be peaceful, you will probably want to go tall, and if you go tall, you will probably have trouble earning faith points, and if your having trouble earning faith points, your religon probably wont be spreading. Not to mention that you can't rely too heavily on it, as if that civ has seven cities converted dows you, you are suddenly in low happiness.
Pilgrimage is such a small benefit that it seems almost redundant. Not to mention it provides a resource that basically becomes redundant by the end of the game. Not to mention the developers know it is bad enough that they need to fix.
Tithe, in my opinion, is better than Church Property and Initiation Rites simply because it does not have to be the majority religion. If you are not actively spreading your religon you still make a profit and, if you are actively spreading your religon, you make a bigger profit. I'm not at deity level, but I've seen the size the AI cities regularly get to 20 population, and this would then provide five gold for that city. Also, I may be wrong about this, but I don't believe those four citizens have to be in the same city.
World Church is better than it looks. Culture is hard to come by, and if your religon reads enough, this belief can almost single-handedly take care of your social policies while you focus on other buildings. I recently finished a Songhai Domination Game on Emperor, and this policy allowed to fill out Tradition, Honor, and Autocracy before the game ended.