Right. The nice thing about Civilization is, is that there is no "silver bullet" that applies to every situation. For example, everything I said in the previous couple of posts would be very wrong in a Sid level game: there you have to crank out the first 4-5 settlers as fast as possible, even if it harms all other aspects of your game. Because if you don't, the AI will have settled all spots around you and you will be playing OCC for the rest of the game (which fortunately will not be that long...

)
But the original poster stated that he was playing on the low difficulty levels (even as low as Chieftain), and I think for this level (and for pretty much all "standard" cases on the levels up to Emperor) the advice I gave will yield very good results and allow the average player to play a comfortable and successful game. Of course it needs to be adjusted to the given circumstances. (Both of us have already stated some examples where adjustment to the "general" strategy is needed: an important resource you need to get under your control, before the neighbor does, or a certain Wonder that is important for your plan for victory.) But the player will learn by experience after a couple of games, where such adjustments are necessary.
I have already mentioned one case where "cranking out settlers as crazy regardless of the consequences" is not the most efficient strategy: when you want to build up a powerful army quickly and then simply capture the towns that you did not found. (To put it in a nutshell: if you build the settlers, you will have the towns. If you build horsemen, you will eventually have the towns
and the horsemen...

-- At least in some situations.)
But let me also comment on another important factor of early gameplay, that we have not yet discussed. Perhaps this is, what you have been missing so far:
the Despotism penalty.
The Despotism penalty hurts your empire really hard: less of everything (though mainly food and commerce, since early in the game you probably have not yet built any mines on hills/mountains whose production would then be affected by the Despotism penalty), and on top of that, this "less" that you have is then reduced by the higher corruption rate of Despotism...

Therefore it should be a top priority to get rid of that penalty as fast as possible and reach a proper government. Now for doing this, you need to research fast, and for this you need a high commerce output. And here we have two goals that more or less contradict each other: the goal to expand quickly and the goal to create high commerce
early. Why is that? Because of three factors:
- If the central core towns constantly operate at size 5-7, they generate much more commerce than if they would constantly operate at size 1-3. (This is true on the lower difficulty levels, were 4 citizens are born content, but even on Emperor, where you only have one content citizen, it is true, if you create the necessary military police and hook up one luxury. But even if you have to increase the luxury slider, this statement is true, if you have enough river tiles or other 2-commerce tiles that the extra citizens can work, because it takes only 1 commerce to keep that citizen content via the luxury slider!)
- When building a settler in the capital, you basically trade two citizen (that may harvest you 4 gpt) for one insignificant town that might only contribute 1-2 gpt. (At least until it has grown and developed a bit, which may take a long time.)
- And finally: corruption again! The strategy of "growing tall" instead of "growing wide" has the advantage that all of your population is concentrated closely around your capital, keeping corruption low. Consequently, if we compare two empires that have exactly the same amount of population, but one has a few size 5-6 towns around the capital while the other one has lots of size 1-2 towns spread out further away, then the "tall" empire will create much more commerce and reach Republic much earlier.
The importance of establishing an
early Republic is underestimated by many. But in my experience, under Despotism your empire grows only linearly, while once you are a Republic, it takes off the ground exponentially...
Also take into consideration: if you are too slow and miss the Republic slingshot, you will be facing an extra couple of centuries under Despotism... (Ok, this applies only to C3C, not to Vanilla/PtW.) So in my experience it is worth it to refrain a bit from expanding too wide in the early phase and in return for that get Republic much faster, at which time you will "explode" and easily catch up & overtake the AI, which has meanwhile deployed the "settler-at-size-3" strategy.
Coincidentally, I just found a short discussion between two excellent players, templar_x and PaperBeetle (who both were #1 in the GOTM ladder at some point of their career) and myself, about when it is better to build the first settler early, and when it is better to let the capital first grow a bit and build a granary (and maybe 1-2 workers) first. See posts #110 and #117-120 in the above mentioned Asterix game. Interestingly, all three of us agreed that the "granary first" approach was better in this situation, even though there were two reasonably good town spots available not too far away (one with a cow and another with two floodplains). The reason simply being that either of those spots would have required lots of worker turns before it would become productive, and therefore it was better to first improve the capital to full potential, before settling the second town. (Unfortunately all my attachments in that thread have been eaten by the forum upgrade a few years back, so you can't look at the situation yourself. I really need to check sometime, whether I can still find the screenshots and sample .sav files on an old disc. That thread has lost most of its value because of the missing attachments.)
So anyway, it's interesting that I am not the only one, who does not consider "cranking out settlers at all costs" to be the top priority. "Becoming powerful" is the top priority.