While I haven't played anywhere as many G&K games as others here yet, I'm already getting the gist of how powerful religion/faith can be
when used right.
About which beliefs are very useful (or pretty much useless), well that's completely situational. Buidling cathedrals with faith and adding growth did wonders for my recently finished cultural win game, not to mention the additional 3 GAs I got with faith. In total, I think I got between 12-14 GAs, two thirds of those burned on golden ages. So, I essentially spent a third of the game in a golden age (including pretty much the entire Industrial & Modern era), adding 20% to my culture output. I had the Taj Mahal thanks to a GE. Massive!
I've just started an Austria game, bagged the Stonehenge with massive chopping around Vienna. Now I just hope the 15% percent modifier with city states is available when I found my religion. If so, aim for the Patronage SP 20% modifer and suddenly every city state you've discovered and isn't at war with, is 'friendly' granting you a massive food/faith/culture/happiness/free unit bonus for the remainder of the game - and you don't have to sink a single piece of gold into them for this. Add the synergy effect with Austria buying selected allied city states for herself pretty much at will and you've got a monster civ.
Where I feel I'm lacking though, is with spreading religion to other civs. Haven't really tried that out yet, figuring out the pros and cons etc.
Edit: your influence with city states aren't calculated in % as I came to write above, but in influence points
