If you want a religion, second or third (first is a dice roll), and you don't yet have a 'feel' for the timing behind things, I wouldn't produce more than one or two settlers to start, and I'd go very light on units. Check the Great Person screen every other turn until you start seeing prophet points being generated, and then check it every turn. Someone mentioned running prayers, and this is sensible, but remember that if you have the time to get a shrine up, its better to build the shrine before running prayers. The shrine will double the GPP output of the holy site while you are running prayers. And that will help combat Russia and Divine Spark. Having a 2:1 GPP advantage is nothing. That can disappear fast. I aim for 3 holy sites and two shrines, and then run prayers if I'm nervous. I've had great days where I can get 3 shrines up, and bad days where I get one and have to burn precious turns running prayers. But I get my religion.
I guess I should mention too, don't waste time researching any unnecessary techs before you go for astrology. You might need mining first if you don't have a patch of land.
God-King is a tough one, and I've tinkered with this choice a bit. Essentially, if you are running prayers, you are generating the faith for your pantheon. And having +1 production will get those holy sites and shrines out faster. But I've found that if you aren't getting faith from another source, yea, you have to bite the bullet and take God-King to have a shot at the pantheon you want. If you don't care about the pantheon (I do), then I'd skip God-King and take the production, and pick the pantheon up as you are generating faith with the shrines/prayers.
The ai WILL purchase great people, make no mistake, so if the race is close, buy the prophet as soon as you can.
If you don't get a religion, faith can be used to buy great people and units. Someone mentioned Valetta, and while I don't usually concern myself with Valetta, I have been suzy of her once, and the boost is considerable. Especially on x2 marathon, which I tend to play. And then you have naturalists. In a current game I can buy a naturalist every 4 turns at the moment, and that is handy if you are going really wide.
Another little tip is that if you research animal husbandry first (and really, if I beeline astrology, I usually find I can research at least one other tech before I start building holy sites), you can hopefully sell some horses for good cash which you then can use to buy shrines. I'm not sure how game speed affects trades, but I get usually get 300+ gold per horse, and in a pinch I trade off 3 gpt for 100 gold - to each ai as long as I have the gpt to swallow. So if you take husbandry first and have horses, you might be able to make a couple of trades before you are done with your first holy site. Obviously buy the shrine in your least productive city.
You could always chop for the holy sites too... but I don't like to chop, and I find you don't have to.
edit: I guess I should mention too that I push hard for religion because I go for specific beliefs. If you only want a religion for a religious vc, I guess you only need to make sure you get *a* prophet, as opposed to the second (or third). My goal is the second.
edit 2: Guess I should also mention... Stonehenge doesn't guarantee first religion. I've sat a warrior on Stonehenge before, and watched the ai's prophet bob and weave for a number of turns until my own prophet had popped. Theoretically, you could put a scout on every holy site/stonehenge you can reach and thwart every ai's attempt at religion.