Too early settlements buildings are a mistake. A new pop grows in 20 to 30 years and all settlement buildings will effectively block migration. I would wait with them until the city has something going, like 30 pops, so in the meantime it is fed with migration naturally from the territories in the province.
Afterwards really depends who I am playing. A religion & heritage with tribesmen bonus means I will put a building in every province which has native consistent hapiness bonus for them, for example. Then, the buildings will follow mostly province specialization, in those better for freemen I will build barracks, in those for slaves slave estates etc. Farm settlements and slave estates, from the pov of food supply is something you need to consider past midgame, until then maybe only Latium and Nile Delta would need support with such thing, in rest is redundant.
Mines I build very rarely, it is usually better to get that extra product with a city, but really depends, can be a thing.
Overall, city first, settlements way after. The only exception is provincial legation which I would build if I have enough money, especially in kind of redundant territories which won't see much action anyway (fur, stone, salt early game etc).
If you want to spend your money on something, take a 10 cohorts legion and build roads through every territory you own, preferably all of them connected to all (so if a tile connects to 5 other tiles, build roads toward all of them, particularly in cities).