Is it better to build a worker/settler or to let a city grow a bit first?

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.

A worker or work boat is the best unit to build immediately nearly 100% of the time. Additionally, you should generally research one tech which will allow you to exploit a resource near your starting city and then research bronze working for the ability to chop-rush additional production, or go straight to bronze working if you can already exploit a resource. Tons of analysis has been done on civ4 and you can find the answers to most questions here: http://www.civfanatics.com/

Specific to this question: http://forums.civfanatics.com/showthread.php?t=165632 http://forums.civfanatics.com/showthread.php?t=234378