Library
My favorite building is Library.
It is very solid and provides a double bonus for whichever role you choose, so the bonus is always there, it is also very versatile, it synergizes with many buildings and gives you options.
The downside could be that it is quite expensive for a relatively minor bonus.
Lets look at the pros by role:
>>Mayor>>
- it gives extra colonist so you get 2 extra instead of one and paired with Villa you get 3 extra which can be huge for Fortress and Royal Garden play
>>Craftsman>>
- you can produce up to 2 extra barrels which can be very strong for Aqueduct-Large Indigo/Sugar Plant-Specialty Factory-Union Hall/Wharf combo, so you can produce up to 7 indigo/sugar barrels which give then 6 db (db=doubloons) for Specialty Factory and you get huge points from Wharf or Union Hall for shippin those
- Union Hall benefits a lot lets say you produce 2 corn and 1 indigo and 1 coffee, you can choose 2 extra so you produce 2 corn 2 indigo and 2 coffee with Library which then give 3 points from Union Hall, if you have Warehouse it can get out of hand quickly
>>Trader>>
- you get 2 db extra from your trade so paired with Markets can be a really big portion of db from a single trade
>>Settler>>
- you can choose 2 plantations, so if you have Forest House you can choose a quarry and a forest or 2 forests with one settler with major discounts on building, also it goes well with Residence and the Forest House play with Cloister
>>Builder>>
- here the bonus makes the required db amount for every building 2 less, and if paired with quarries/forests it can be a major discount
example: you have 3 quarries 6 forests and a Zoning Office, if you select the builder you can crank out a large building with havin 0 db in your possesion
- point is it is easy to build even with only 1-2 quarries
>>Captain>>
- you get 2 extra VP from your first shippin so the points may come handy and synergizes really well with Harbor
>>Prospector>>
- you get at least 2 db and sometimes 3 and very rarely even more and with those you have easier time to build
So what I like to do with Library is goin the builder route and get up to 3 quarries if possible also Forest House for 6 forests and if possible pair with Zoning Office to take db from prospector and try to crank out large buildings where the Church can also really help
Is it worth the price?
Sure the price is steep and you can say you could use the db better somewhere else, but if you have 2-3 quarries and a Zoning Office it can payout.
The earlier you get it the greater your benefit, so I dunno.
I usually try to build it, so to know for sure you have to try it out yourself.