@ Rambuchan - I usually don't grow my cities that fast. In despotism cities almost never grow because you are building lots of workers and settlers, and in despotism and monarchy you can use MP if necessary, so we will assume we are a Republic. You really need cities to grow to at least 7 in Republic for unit support. In Republic, each citizen should produce a minimum of 2g based on working a roaded tile, some will hopefully produce more (river, coast, or some bonus). If you have 7 citizens, the city should be producing at least 18g (2 per citizen plus 4 for the city tile assuming no corruption). Assuming emperor level or higher, you get 1 happy for free. If you have no luxuries, you need 40% luxury spending (ouch!). If you have 2 luxuries (which shouldn't be hard to get, and is really an absolute minimum for survival in Republic), then luxury tax has to keep only 4 people happy and can be lowered to 20%.
My cities typically won't get much larger than 8 early in the Republic years - it does become expensive, and also at that point, you still need lots of workers, so I will often skim a worker off on growth to 8. By the mid to late Middle Ages, I would expect to have a minimum of 4 luxuries (via trade if I can't get them myself) and a marketplace which provide 6 happy faces. If I want to grow to size 12, my city will produce a minimum of 28g so to keep the other 5 content, I still only need 20% luxuries. A fifth or sixth luxury, and you have no problems at all.
Of course, all of this is written from a single-player perspective. I have no idea how easy or difficult it will be to acquire or trade for luxuries in this game.
@fe3333au - for cultural expansion, we will build libraries