This is the build order I’ve developed for early game cities. I make no claims to optimality; it’s just what works for me.
1. Something to enable border growth. Usually Monument, occasionally Smokehouse if the location calls for it.
2. Faith generation. Usually shrine, but if my pantheon gives Faith to another building, I’ll build that instead. If I’ve already founded a religion or am close to founding, I’ll skip this step.
3. Well/watermill
4. Anything that boosts local resources/improvements (smokehouse, herbalist, stone works, forge, etc.)
5. Council/monument (if not already built)
6. Forge/barracks/arena
Everything after that is context-dependent and based on what my empire needs.
I weave in settlers, workers, and military units as needed. Purchase them if possible, otherwise build them in high-production cities.