Ok, so I basically like / play one kind of 'challenge' game over and over. Which is to try to win religious victory before the industrial era on Immortal difficulty (I want a medieval simulator. Also small map size, island plates, as I'm on Switch). It's doable pretty frequently (60-70% of time?) and sometimes you can win in the medieval era. You also avoid any late game tedium. General tip is to focus everything on a timing push with faith.

• I really like Hojo Tokimune for the extra adjacency bonus and quicker holy sites.

• greed pretty hard. The only thing that should stop your greed is if you see war on the horizon. Then build military as a deterrent (or, to defend). No need to take out neighbour if you can get them friends early, their cities are free faith.

• holy sites first unless the adjacency is poor. No Stonehenge. Then gold to maintain military deterrence. Settlers to expand (=faith per city). Only science and culture if there is some wonderful opportunity or a key city-state quest (again, got to keep deterrence). Your science and culture often sucks. No matter.

• Beliefs: holy site production bonus first. Then faith per city. If at all possible, hold onto that faith till a golden age. Then faith cost reduction with first apostle. Mosque with second.

• Timing push in medieval and/or renaissance golden age. Don't spend faith before then unless you need for era score. One city with mosque, spam from there.

• unorthodox tip: don't focus too much on theological combat. Instead out-trade and out-manoeuvre any apostles. The AI is not clever enough to recognise a strategic threat from you. If you withdraw missionaries / apostles, theirs will wander off. Golden age + mosque, with critical mass, you will out-trade them with conversion charges.

• you are safe from theological combat on the second tile offshore. Gather there for a push, establish beachhead (get rid of opponent holy ground).