It's like Taedius said how you build your economy depends a lot on your style of play. I prefer (like in all games were this tactic works) to invest all money I can get to build my economy up first. I often fight only with levies or medium troops because I build nearly no barracks in the first time of a campaign. I really hate it when I don't have the money to build in all cities without a break.
If you play with huge units like me the growth of your cities is really important. I usually build drainages and healers at first often followed by farming "buildings". Every health bonus will increase pop. growth with 0,5% and public order with 5% and a farming bonus will increase pop. growth with 0,5% and provide some more farming income. That's because I prefer health bonus in cities with lower public order.
As trade is a really important part of your income you should build trade ports and paved roads as fast as possible. There are some provinces where trade income is low and you may prefer to build other things first. To test the effect of a building open the city details and then click on the building, that's the best way to see how much it will benefit you.
As your empire grows the corruption will become a proplem since it increases with the distance of a city to the capital. That's why buildings (especially temples) with law bonus become more important because the law bonus lowers corruption. I prefer to build the temples with the best happiness and law bonus in nearly all provinces.
Mines provide a good income especially in provinces with 2 or 3 gold/silver veins, if you have the money and time to build them, do it.

I hope this will help you a little bit.