My general game plan when it comes to districts is as follows:
Spam: Commercial Hubs and Harbors
Build at least one: Entertainment District
Build at least two: Campus
Build at least three: Industrial Zone
The Entertainment District ensures I can build the Colosseum, and it almost always goes in the capital. The Campuses help with science and let me get eurekas for Astronomy, Printing, and sometimes Education, and I usually get more than two, but I tend to reserve them for the juiciest spots. Three Industrial Zones are enough to ensure the cities that matter can get the factory bonus and they also let me get the eureka for Industrialization.
Everything else is situational. If a particular district is necessary for the victory condition you have chosen then spam it, but otherwise they may not be necessary and may even be a huge waste of cogs and a precious district slot. If all you want is raw culture to advance through the civics tree Theater Squares in particular don't pay off well, imo, and there are policy cards that will provide adequate culture (Trade Confederation and Meritocracy) for any other VC. Holy sites are a complete waste unless you want to try an RV, imo, and you can capture plenty of Holy Sites from the AI if you want some faith income. Campuses for raw science are subject to diminishing returns, and I only spam them when going for a science victory.
Encampments are a bit trickier, as even if you aren't playing a dom game they can still provide useful cogs and housing to cities in poor (few hills and/or no water) locations and may sometimes be worthwhile. If you are playing dom, or suzerain of Carthage, then obviously spam them, as Great Generals are awesome and so are trade routes.