What you build is dependent on what you need in the province.

church/religious buildings:
Not necessary in province where the population is already your religion (unless you want extra priests). You will be better off building an inn, as it also provides happiness for the nobility as well.

School:
Whilst it is nice to have lots of school so you can research lots of things simultaneously, it does not mean you need one in each province. They bring down happiness which usually means a inn/church is required to cancel its effect, reducing room for workshops, which bring in money.
Depending on how well your empire grows, I found that most of my schools come from captured regions. After 5 or 6 schools, I start even demolishing them in newly captured regions, unless it’s a modern university (which you can only build in your capital).

Inn:
I only build these when i require the happiness boast. For cities that need heavy garrisoning, it is much cheaper to build one of these then pay massive upkeep on the troops stationed there.

Workshop:
They are a great source of income. I try to build as many as i can without sacrificing research whilst maintaining happiness.

Port:
Fishing ports are a great way to increase population growth. (Just remember to replace them with ports once maximum number of towns in the region is reached)
Trade ports are always useful, however it maybe necessary to built a shipyard to build your navy.

Admin slot:
I usually build the non-military ones in continental Europe, as there are plenty of region that can build barracks. This is often not true in the Americas, in which cases, building military ones are justified. I am not sure about the case in India. The admin version provides more income and greater repression.