Yes it sucks that in Civ VI you can't really go tall (unless playing the Maya, and someone said maybe 1 other civ? IDK). I think if you're going for a PEACEFUL game, the best number of cities to shoot for is in the range of 8-12. You do still want quality over quantity. I think it's ok to settle 8-10 cities early, and then after they're developed, go and settle a couple more in bad places just to hit 12. The nice thing about 12 is that going any more than that will require more luxury resources, as they can only go to 4 cities each. So having 13 cities you'll need as many luxuries as 16 cities, assuming the cities all reach a decent size (cities need amenities starting at size 3, except your capital (I believe it starts at 5), and then every 2 population after so it REALLY adds up).
What you build and in what order will depend largely on your civilization, map type, and just how the game is going in general, but an overall good strategy is to START with a slinger (I don't know why so many people suggest starting scout; yes, they can explore better, but a slinger will help more against the barbarians, which WILL be a problem as you saw). You do NOT want to start with a builder because there will unlikely be much they can do early. In fact, I hardly EVER build builders. Why? I buy them with gold. Just every time I get enough gold, buy a builder in the town that most needs it. Other than that focus on other things in my cities as I go.
One way to help you get more gold is to settle on a luxury resource, if you can, but don't go too much out of the way to do it if there's a prime option elsewhere. Also, a lot of times you can buy a builder, have them get a luxury resource, and then sell the luxury resource to basically make your money back (or a good chunk of it). In emergencies you can use gold to buy units too, and you'll always spend some on buying tiles. But the majority I use on builders in the early game.
Anyway, after I build the first slinger in a town you should be around population 2 by then. So I build a settler as my second thing. It's usually safe to do so, but keep barbarians in mind. While you're doing all of this, you should be going down the civic tree trying to get Early Empire ASAP. Hopefully you'll get the civic boost by discovering another continent -- it's your discretion whether you want to keep going down that route if not or swap to the other one until you do -- but the 6 total population won't be hard to do with the 2 early cities.
I would always use the policy slot that gives you +1 production in every city, unless you get a boost of faith somewhere then swap to the +1 faith one. If you're lucky enough to found a pantheon early enough to grab the free settler, I would do so; otherwise, just keep 2 cities until you research Early Empire.
The 2nd city (and 3rd, if you build it in time) I would have start off with a granary, ESPECIALLY if they're not on a river or lake. (If you can't build a city on a river, oasis, or lake, try to at least build it on the coast.) It looks like you built both Athens and Argos not on a river/lake/oasis........that's bad. It's not worth it. You lose FOUR housing by doing that, it's just not worth it. Aqueducts aren't worth building, and regardless, you can't even build them in the early game. Just don't do it...
If you built your 2nd city on a river a granary is less important for the housing, but the growth it provides is usually still worth building it.
Your capital I would have build other things; perhaps a wonder if you think you can swing it, an early Holy Site to found a religion, or an early Campus and Library for a science boost.
Once you research Early Empire, I would have BOTH your 1st and 2nd cities spamming settlers as much as possible until you reach that goal of 8-12 that I mentioned earlier. If your 2nd city is much slower than your capital at doing this, you might only have them make 1 or 2.
As for districts: You want to think about what your overall plan is, and then decide what district you want in each city. You want every city to have an Industrial Zone, Harbor or Market, and one other district depending on your planned victory type. Big cities will get at least one extra district on to this to specialize them in things you are not specialized in. But this does not mean Aqueduct. In most cases you will NOT BUILD AQUEDUCTS unless it is absolutely necessary. DO NOT PLAN your cities with an aqueduct in mind unless there was no better option. Just don't do it!
Unless you're playing as Germany (which gets an extra district per city) you get a district at size 1, 4, 7, 10, etc. (every 3 pop). One neat trick you can do is place a district as soon as your city hits that next size threshold, but then go back to building whatever you were before. The reason for this is that districts get more expensive as the game goes on, but the price is locked in place once you place it. You could safe dozens of hammers and shave off a few turns building by placing your district before you're ready to build it.
So again, every city gets an Industrial Zone -- just too important not to. And every one gets a Harbor OR Market but NOT both (they don't stack trade route capacities). Harbors are generally better, especially if the city is on the coast, but if it's 2-3 tiles away then Markets are probably better (or of course more than 3, you can't build a Harbor!). After that, you want Theatre Squares if going for Culture (or Diplomacy*), Holy Sites if going for Religion, or Campuses if going for Science or late-game Domination victory. For ealry-game Domination, I'd focus on Encampments or Stables, but then start building Campuses if you failed your Domination efforts early. AFTER You have those 3 base districts in each city (Industrial, Harbor/Market, and specialized) then your cities that hit size 10 can start building the other districts. A centralized city or 2 will want an Entertainment Complex, a Government Plaza needs to be somewhere, a few Campuses could help for any victory type, a Holy Site early even if you don't want Religious victory doesn't hurt, and a Theater Square or 2 even if not going for Culture just to help with the civic tree and prevent opponents from winning Culture.
When should you build an army? When you feel threatened. Try to do it BEFORE someone prevents war on you, but if it doesn't seem like they will, no need for an army yet. As your capital is cranking out cities, you could have another high production city focus on military OR buy them with gold. Districts are kind of just what you build when you are more settled (have your cities and your army), but certain strategies might have you needing to build some earlier. Also, there's no shame in building an early Encampment or Stable, but try to make sure it's in a city that will hit population 10 so they can get the important districts later.
Do you conquer neighboring city-states or no? Well, if you have an army it's easier but you'll make other civs angry. It's up to you, but usually I don't do this. The penalties for taking a city-state outweigh the pros, IMO.
I planned on building BOTH a campus and an industrial zone, but based on what you're suggesting I don't need to go too crazy with science districts as I do with production/hammers/cogs. I am playing as Greece, so I do intend to build the culture districts in every city possible after those initial bases are covered.
