Democracy is over-rated. The ONLY reason I would switch from republic to democracy is if I really needed the faster workers. The difference in corruption between republic and democracy is minimal (barely noticeable) and isn't worth 4-8 turns of anarchy. And the difference in corruption is negated if you have to increase luxury tax because of War weariness.
As for the monarchy-republic debate: Republic if you want more money/science (in most cases) and are peaceful, or have short wars. Republic earns an extra gold piece from every tile that already is producing one, so basically you are nearly doubling your money. This confuses some players because they panic that they had to lower their science rate from 90% to 60% when they switched to Republic. But even though the rate is lower, MORE money is actually being applied to science, so you have to pay attention the actual gold being applied and not just the %. HOWEVER, luxury rates, and paying unit costs will drain Republics commerce bonus. So if your luxury rate is too high and you have way too many units, then Monarchy may have been better for you.
Monarchy if you like to wage many long wars or you are really short on luxuries. In monarchy your cities can support up to 3 more citizens, by using military police. If you do 'pointy-stick' research where you depend on beating techs out of your neighbors, then go to monarchy. If you have access to 0 or 1 luxuries then monarchy would be better (except for maybe chieftain level where you already get 4 citizens born content). If you have 2 luxuries it is more of a debate whether monarchy or republic is better, but having 3 or more luxuries (and especially if you have marketplaces), then republic is easily better.