I suppose it depends on the race of the natives. Might be that you get some cool new units if you build it up...

I'd say it depends on whether or not you need money now, or a lot of money later. If it's early in the game and everyone hates you and you're already at war, I might delay economic development and focus on trade goods until you get some breathing space. If you're isolated on an island or on Myrror, and if everyone loves you, it's probably worth building.

I don't think there's a single correct answer.

For settlements, I wait until there's at least a population of 2, then I follow your basic plan. Since I'm presumably garrisoning them with units from my capital, barracks construction can wait until after I've developed a solid research/magic/production base.

Conquered cities are much the same, but I may get shrines, temples, animist's guilds, etc. built even sooner to reduce or eliminate unrest. If I have the money by that point, I'll start using it to get things built quicker; if not, I'll temporarily throw the city into production mode and/or raise taxes overall.

Protip: If you're good at micromanaging construction, he most cost-effective way to build things quickly is to wait exactly one turn after starting each new structure, then paying for the rest of it in full. This is, in effect, a better than 25% discount on the cost of construction! If you're in even less of a rush, the next discount level happens when half or less of the structure remains to be built. Besides the obvious troop movement benefit, roads provide a small production bonus between the cities involved, which translates into more gold; this bonus is actually somewhat higher when the cities involved are of different races. (Coastal cities get a similar bonus, even if they have yet to build so much as a shipwright's guild; the ocean is presumed to be their road.)

Actually, the construction buyout is even more exploitable: nothing stops you from changing the active project once you've bought it out, so you can buy out a 10-production item, then switch to and buy out a 20-point item, then a 30 or 40 point one, etc - depending on what buildings and units are in the list, you may be able to buy every building and/or unit for just over half price (since the initial item will cost more).

I... I am ashamed that I never figured this out for myself.

Even more evil... buy a building that has a production cost just under what you actually want. Then switch to the actual building you want, and adjust your production so that it finishes in one turn. You didn't have to pay that last 20 or 30 production!

For example, if you want a sawmill (120) and can have 20 or higher production per turn, buy a shrine (100). Then switch to sawmill and your city will provide the last 20 production and it won't be wasted!

Far too much micromanagement for me, haha, I never do this.

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On original topic, I build the basic structures Gerin recommended (except sawmills), plus librarys and shrines. After that, I build temples or parthenons based on unrest. However, I am an extreme expansionist, so all cities are contributing to engineer and settler construction for quite a while. Settler construction keeps unrest in check, so those basic structures are all I need until I stop expanding and start to grow cities.

Once I get a strong economy, I tend to buy a lot of those early game buildings (Builder's Hall, Granary, Smithy, Marketplace, Farmer's Market) the moment an outpost turns into a town.

It depends a lot on which race you have in the city, too. Some of them grow fast and some grow slow. It also depends on what kind of wizard you're playing, because if you have access to some of the city augmentation spells in the Life books, that changes the equation. If you have Dark Ritual from the Death books, you'll want to build every religious structure you can in order to maximize the effectiveness of that spell.

I always try to buy granaries if I have the money. They only cost 160 starting from scratch. Just doing that seems to make my cities grow faster.

If a city has a lot of forest squares I'll build a sawmill first.