A study for you: (actually, I didn't know all this before either)
Here's the results of an investigation I did with one of my better cities in which I have the mrktplce, bank, lib & university built. Then I sold one at a time to measure their effects. BTW, I'm running a republic right now.
I have an overall tech of 70%, Luxury of 10%, which leaves 20% as income. The production of the city is 77 shields.
My actual funds allocated are as follows (the Wealth amount refers to how much a wealth production added to my overall treasury income. It was determined by changing the production back & forth from wealth to something else):
Treasury Science Happy Wealth
22 78 6 19 - with all improvements
16 78 6 19 - after I sold bank
16 58 6 19 - after I sold university
16 39 6 19 - after I sold library
11 39 6 19 - after I sold marketplace
Conclusions I would draw from this:
- Wealth production is unaffected by your commerce improvements.
- The amount of help you get from a commerce/science improvement is dependent on your commerce/science rate
So, based on this, I would say:
- build the improvement that would help you most at the time. For example, in my case, with a 70% science rate, a university contributed 20 beakers where my bank was only contributing 6 extra coin.
Of course, this doesn't take into account that perhaps in the next turn, I'd change the tax rates and then a bank would be more valuable than a library. Also, the cultural impact of an early library is pretty significant along with the happy faces brought in by the marketplace.