Let's talk about Founder Beliefs.
First we need an example game situation so here it is: Mediaeval period, Kongo owns 10 cities of 10 pop each, each AI civ owns 5 cities of 10 pop each, one human player 5 AIs, 4 religions in game. All relevant districts have been built.
The 4 AI civs with religions have complete control in their own cities, you and the other non-religious country have a roughly even distribution of each. There's also 2 city states following each religion.
(Forgive these arbitrary madeup numbers, they'll make more sense later).
You can use your Apostles from one of your cities to convert your other cities. Basically you find your Hindu city, finish a Mbanza there, use that apostle to convert another city to Hinduism, build a mbanza there and get a fresh Hindu apostle, etc etc.
Essentially you can pick your religion, so long as someone else got you started and use your potentially infinite apostle spam to convert the world. (Infinite Apostle spam = forward settle a city, chop a theatre and mbanza then leave it for the AI to conquer and after he does raze that city and start a new one).
I would guess that you can prevent the religion's founder from winning by wiping them out (assuming a dead civ can't claim a posthumous religious victory) or maybe just refrain from going all out.
The founder beliefs are mostly straightforwardly mathematical so let's look at the incomes given, using our example.
Church property: +20 gold. (Approx 10 cities, 2g per city)
Lay ministry:+10 culture. (Your 10 theatre squares give +1 culture each).
Papal primacy: +10 science/culture/+20 gold per 3 envoys you've spent rounded down. (Assuming you're spending a max of 6 in each city state). By the late mediaeval this is probably about 6-9.
Pilgrimage: +12 faith. (Approx 6 cities following the faith in other civs).
Stewardship: +10 science and +10 gold. (+1 science from each campus, +1 gold from each commercial hub).
Tithe: + 25 gold. (About 100 pop following the religion, 0.25 gold per pop).
World church: +20 culture. (About 100 pop following the religion, 0.2 culture per pop).
The numbers change a lot when you go converting. If the whole world follows the religion you've picked but the founding civ is dead and so can't claim religious victory these are the numbers instead:
Church property: +86 gold.
Lay ministry:+10 culture.
Papal primacy: +10 science/culture/+20 gold per 3 envoys you've spent rounded down. (Assuming you're spending a max of 6 in each city state). By the late mediaeval this is probably about 6-9.
Pilgrimage: +25 faith.
Stewardship: +10 science and +10 gold.
Tithe: + 107.5 gold.
World church: +86 culture.
Looks to me like World Culture is the best. Get that in one of your cities, finish a mbanza there, use the apostle to convert more of your own cities then use a wave of apostles to convert most of the world without accidentally handing a win to the AI that founded the religion, picking up a few relics on the way.
Other strategies are possible, you could for instance pair papal primacy with an Apadana/envoy strategy.
Another fairly obvious use of your apostles is simply to prevent someone else winning a religious victory.
To give an example from my current game. I'm playing India and didn't get a religion. The AI civs have the following:
Spain. Catholicism. Church Property.
America. Protestantism. Papal Primacy.
England. Buddhism. None yet. (I blame Brexit).
Scythia. Conficianism. Lay Ministry.
Norway. Zoroastrianism. None. (That might be kinda my fault. Oops).
Church Property is probably the pick of a bad bunch. So if I were playing Kongo instead of India I'd forward settle Spain then build a mbanza after they converted that city.
(Afterthought. I've been struggling to get my head around a good Poland strategy. You need to go heavily into Holy Sites early on to contest the great prophets but you also need strong culture to unlock Winged Hussars on time. It just struck me that this might be the way to do that. With World Culture you can basically get culture from faith points).
I think the tile still had a road, though. This was a couple patches ago, and it may have changed since, but my guess is that this is still the case.
I thought I had figured out a fun new strategy.
