Should I be working production tiles early?

[ShinigamiKenji]

A Slinger is 35 production, so you almost built another Slinger (Archer for all practical purposes) with this accumulated production. If your plan include rushing a neighbor (which is often the case), then you saved up ~10 turns from an early rush. That might be enough to conquer 1 or 2 more cities before walls are up, and it just snowballs from there.

At the same time, if you start isolated from all other AI, then you really wasted your time there.

It isn't an easy task to quantify the impact of such decisions at the beginning of the game. It isn't just the number of cogs, you need to factor in opportunity costs too.

 

[Ribannah]

As a general rule, food always comes first until housing / amenities become an issue, except when:
- you can finish something important one or two turns earlier (especially something that gives more food)
- you're building (or going to build) a Settler, since you want that to finish before you gain a pop.

Note that when your city gets to size 4, you can lock the production costs of a second district by selecting its location.

 

[Jarms48]

If I have a decent enough start I'll focus on food until pop 4, then I'll focus on production. If I have a bad start I'll focus on production to get an early settler and hope my second city is better.