I'm curious about your opinion, what buildings do you think are useful in a province (castle or city), in which order and why.
On the other hand, what do you think it's simply not worth to be build and for what reasons.
I think it's important (especially for new players but not only for them) to know, construction-regarding, what's gaining and what's wasting money in this game.
Personally, in a town I start with Dirt Roads (for units speed and trade), Port (ports are actually the real money-making buildings, better than everything else. Just try it in Stockholm to see the before/after huge difference, it's a complete game-changer for that particular settlement), Land Clearance (growing population), Grain Exchange (merchants and trade), Mines (if I'm lucky and I can build them), Merchant's Wharf (where available, it boost your trade), Town Hall (if I don't have any in my kingdom, that's the first building I make, as I desperately need to start pumpin' diplomats asap), Town Watch (for pop happiness and militia units), Small Church (only if the Pope demands it, if I want to improve a governor's traits or if it's too much religious unrest in that province; otherwise, I skip it for later) then I upgrade city's walls and make the next level of the buildings from above (plus Brothel + Inn for the town in which I plan the Assassins Guild, usually it's Dijon when I play in the west or Zagreb in the east).
Later, only if the situation demands it, I build the Ballista Tower-chain (border provinces with high risk of invasion), City Hall and Mayor's Palace (if I'm forced to raise tax-level, if squalor is high and population unhappy. Those buildings are useful for merchants and diplomats also), Militia Drill Square and above (same reasons as City Hall, plus military units, minus merchants & diplomats).
Also on dangerous border-towns I build a Leather Tanner and a Blacksmith, just to boost my militia-garrisons.
I think it's a waste to build any military buildings (Towers, Tanners, Ballistas, Gunsmiths etc.) in a city that's not gonna be on the front-line forever.
Also, Naval Drydock, Great Market and Merchants' Quarter are not worth the money if you're not expecting at least another 100 turns ahead 'till victory.
Neither the Tavern or above.
Not a big fan of the churches, too. Especially that in cities where you produce merchants from, it's not good to make level 4 or 5 churches (no Cathedral or Huge Cathedral, Jama or Great Jama respectively) or else there's a chance your merchants will get -1 finance (I forgot the name of that trait). Except the city in which I'll make the Theologians Guild, I don't bother to make even the second tier of churches (unless Pope specifically asks for that).
Regarding the castles, at first I build economical (roads, clearance plus ports and mines - where available) and after that military buildings. Especially Stables and Jousting Lists (since I find myself quite capable at leading cavalry on the battlefield) but also the Leather Tanner-chain and, if the situation determines me, infantry & archery buildings. But usually I try to build only what I really need.
If the province is in a dangerous place, I try to develop it to Citadel asap (a high-chivalry general appointed as governor there really helps with the process), if it's away from trouble I concentrate on other settlements.
But enough about me, how about you?