Since the city doesn't grow when I build a worker or settler I find myself wondering whether I should build a barracks (and granary if I can) first before building a unit.
What's more efficient?
Civilization – Is it better to build a worker/settler or to let a city grow a bit first
civilization-4
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Best Answer
Typically your first build should either be a warrior/hunter, worker, or settler. Don't build buildings right away, the bonuses you get from them early on aren't enough to offset the slowdown in exploration and expansion.
While it might seem like you are slowing yourself down by building a worker or settler first, keep in mind that the city tile itself is always worked. So as soon as you have built two cities, you are working 4 tiles, at about the same time as your one city would've achieved this by growing to size 3. Fast forward to when both your cities grow to size 2, and you are working 6 tiles, much faster than if you had tried to let your city grow to 5. And the gains continue to amortize from there.
This is especially true if your initial city has a space with extra food/shields to build the first settler faster.