My take...mainly referring to early/mid-game...oh, and welcome to CFC:
I am wondering what the ideal growth of a city is under normal circumstances.
I'm an IMM level player, but I don't get heavy into math in the game. There are other folks that will be able to give you specific details and calculations. However, I will first point that FOOD and growth is obviously very important in this game. I think it is safe to say that it is the most important thing. You will often hear experienced players say, when evaluating the start of some forum game posted here, that a good start should have at least 2 solid food resources (think corn (wet hopefully) or fishes if coastal).
The purpose of growth is twofold. First, it allows you to grow faster onto productive tiles, i.e., bonus resource and mines. Second. FOOD is production. This is an important concept and plays into the importance of Slavery and whipping in the game.
Ideally then, you want at least a +5 or more food surplus per turn in the early game in most cities. This allows you to grow fast and grow back in just a few turns after whipping - even faster with the granary. Granaries, by the way, are the most important buildings in the game.
Obviously, this surplus decreases as your cities get bigger since more food is required to grow and you start to work food deficit tiles. Cites grow faster when they are smaller and the speed of growth decreases the larger they get. This does not mean you don't want larger cities later in the game, it just means that slavery is more optimal when cities are smaller and, therefore more effective in the early game. Late game, you will have better improvement like workshops, windmills and watermills that decrease the need for slavery. It is pretty logical when you think about it.
What is a good city pop to have before you focus fully on production?
I'm not sure there is a definitive answer here, as it can be quite situational based on the land you have and other things like techs. I assume you mean by this question that you focus less on using Slavery and more on the hammer tiles citizens work. Some cities may rely more on Slavery to get up infra while others will be hammer strong and possible lacking in significant surplus food. IMO, what matters is a) your ability to grow based on happiness and the improvements you have in place or available. I usually don't start moving away from slavery entirely until I have workshops and windmills in place and the hammer bonus techs (Guilds, Chem, Rep Parts, etc). I have no answer as to an ideal size of the city at this point, but I think at least 10 pop or more would be good and the more the better. Some cities never grow very large based on food, but can still be quite productive.
Also, some cities simply won't be whipped as much as they are already fairly hammer strong early anyway. You capital is often a good example of this in many case. You will generally avoid whipping the cap too much early for multiple reasons. For one, a bulk of your research in the early game generally comes from the cap plus your first 1 or 2 Great Scientist. There are certainly exceptions to this, but it is a good guideline I think.
How many food resources should you settle around (another thread said 2)?
I think they were probably referring to the Capital/start. Otherwise, it depends on the food resource. Generally, with a good food resource like corn, 1 should be enough to be worth settling as long as you have other good stuff around, i.e., bonus resources, rivers, hills, etc.
However, an important thing to note is the difference between early game and late game. Often early game, your cities will simply be quite small for a long time - no more than 5 or 6 pop and maybe smaller. In this case, I even overlap cities such that they can share food resources since you can adjust tiles or work specialists (which you should be doing anyway) in order to curb growth so as not to exceed your happy cap. This allows you to maximize production and other things at smaller populations which is always the case early anyway.
Now a GP farm should ideally have at least 3 good food resource if at all possible. Sometimes you just don't have a site like that, but you try to get one if you can.
If I am going wide, do I try to keep everything under 4 pop?
I'm not sure I understand the question. I think you mean that your a rexxing - rapid expansion. Keeping smaller pops could help with maintenance costs. However, you have to base it on what you can get away with or what is optimal. I'm not going to limit growth if I can get away with. For instance, FIN or Organized leaders can likely deal with rexxing and larger pops. Also you can simply grow larger and use the pop for production by whipping. I would not just stall growth but instead use the extra population.
What sorts of decisions do you make, and what are some general guidelines for the various victories?
For the first part of this question, I will simply state that I try to keep my empire as compact as possible in the early game. I'm not saying I don't expand, but rather I try to use overlap as much as possible. This allow me to share resources and reduce maintenance costs due to distance. Works great for bonus food and also to switch citizens when whipping such that...say...a gold or gem tile is always being worked by one of two cities.
The second part of your question is much deeper than the general line of question here and I suggest reading some of the articles in the War Academy to get strats on different victories or post a game here and play along trying to achieve a specific victory and folks will help out.
edit: I will also add that you may have situation in which you settle a food poor city for the purpose of grabbing a certain resource. A good example is a tundra site nearby with silver. You might have this city just work the silver for much of the early game - it is worth it. Another example is more watery maps in which you build the Great Lighthouse. In that case, each coastal city you settle pays for itself and more regardless of the food and/or resource available. The point being that although we've discussed here some sort of guideline regarding food, it doesn't mean every city has to follow it. The most important thing is that you are getting "something" out of each city you settle.
