I'm a mere Emperor player so what I can say is only worth that much. From my experience, you shouldn't go Progress if you want a religion. Unless you're a very specific civ with very specific bonuses (e.g. Carthage), or you've an exceptional start for your pantheon.
This is because Progress doesn't have much to help founding a religion. Its only indirect bonus is faster tile improvement, which translates into having your faith-generating improvements up earlier in case your pantheon gives some.
By contrast, Authority has two main advantages:
1) It allows faster land-grabbing by making barbs more manageable and providing a free settler
2) Its
bonuses come faster that Progress', although they tamper down on the long run, while those from Progress (building speed) stay very relevant. In the early game however, Authority provides 1
per policy while Progress provides only 2
for a policy which is usually taken third.
So, with Authority, you can found more cities in the crucial early game, and each of these can have its shrine as well as a possible other faith-generating building (such as a market for the Springtime pantheon) up earlier.
As for Tradition, it has a faith-building of its own. A large capital can also help leveraging your pantheon by working tiles.
And I forgot something: since Progress tends to lack culture early on, I typically build a monument before a shrine in my capital. This is another crucial delay in the religious race.
Therefore, I wouldn't take Progress when playing a civ that really wants to found a religion. Progress is better tailored for when I don't plan to divest much resources in faith stuff. Moreover, I think it has a slowest very early game than the two other trees, all the while scaling much better later on.
All in all the ideal situation for Progress is the following, in my book:
1) A long-term plan to go wide. Otherwise, Tradition is better.
2) Not too much military pressure from neighbors (as in, not starting next to Attila or Shaka). Better to be a Tradition turtle or an Authority pit-bull when having terrible neighbors.
3) Not too much settling pressure from neighbors (hello Pocatello) although it's usually less of a problem than the above point. Expansionist but weak neighbors can be dealt with more easily than militarist ones.
4) An external source of culture (from luxuries for example); this is clearly not mandatory but it helps alleviating Progress's low early culture.
5) No plan to go religious, baring some specific cases as mentioned earlier.
Based on this, good civs for Progress are non-tall and non-religious civs, as those tend to be better off with other trees... and that's about it. Progress can fit any other civ well, really. An early UU definitely helps alleviating Progress' squishiness, but late-blossoming civs such as France can benefit a lot from Progress' boons once they start expanding, as long as they didn't stay too small before.
As for the "top civs" for Progress, they've all been mentioned in the posts above I guess.
EDIT: also, one reason why Authority allows faster land-claiming than Progress is that the opportunity cost of halting growth in your capital by chain-producing settlers is lower. Indeed, to fully benefit from Progress' opener you want to grow your capital in the early game. Later on these yields don't matter. This is another reason why Authority is better for the religious race.
.
gained with UA is worth way less for 9 cities than 4 cities.
in capital to fully use their UA/UB. In general it is advised to play tall as Assyria until you can pop lvl4 units and then just go on conquer spree. I disagree with that, as I believe Progress is better for conquer than Authority and (especially) tradition, but that's just an opinion. Most people agree there are better choices for Assyria than Progress.
