what difficult level are you playing at?
As other have said it really depends on your goal, and what you need the most to meet that goal. The higher the difficulty level, the more important it is to make these decisions carefully.
Universities are probably the most important building in the game. Getting these up ASAP and filling the scientist slots is the best way to generate a lot of scientists to power through the later techs.
Factories are a must in most situations. Make sure you acquire enough coal to build them in all your core cities. They are especially good with a wide empire that goes order for +25% science.
Happiness buildings are important during this phase to keep your empire growing steadily, therefore improving your economy & science.
In general, the later specialist buildings like stock exchange, public school, etc. are not as important as the earlier counterparts. They are very expensive to build and since they come later, don't have the same impact. They should only be built in your core cities that will get substantial benefits from it. For example a capital with monarchy, the commerce opener, national treasury, etc. would benefit substantially from the stock exchange.
There are exceptions of course. Say you are in a very tight science race, you'd want to build more public schools than you would otherwise.
