I play religion as an all or nothing, if you're not a religious civ you're better off putting that production and districts elsewhere.
For example, my last game as Russia I went for a faith purchasing strategy, I took Dance of the Aurora and managed to plant 3 Holy Sites capable of getting a +7 faith adjacency bonus (with the civic card those became +14). The rest of my city plants I tried to get at least 1 tile of Tundra in the 2nd or 3rd border ring, with most adjacencies around +3 to +5 faith. I rushed Theology and then spammed military units, using a mixture of gold purchasing as well.
When it came to additional religious beliefs I choose ones that increased my yields, as I wasn't going for an actual religious victory:
- Work Ethic: I could have went Jesuit Education for synergy, but I wanted to save my faith for just units, so instead I went for increasing my production until Theology was available
- Cathedral: but in hindsight I should have just gotten the Synagogue or Meeting House, as the thought I had whilst playing was if I couldn't get a domination victory I could use my faith to defend myself while pushing for a culture victory (and because I had an over abundance of great writers/artists/musicians)
- Papal Primacy: Probably my favourite religious belief, I found a faith city-state and so I placed all my envoys into it. I was getting an extra +9 faith in my capital, and +6 faith in my other cities
I can't remember which Enhancer was, I think it was Holy Order, just because I wanted to spend as little faith as possible.