First of all, unless you know what you're doing, don't use any courts apart from just courts, as most regions only need just courts.
I am curious what has led you to this conclusion -- my experience is that a region with just above average taxes and with good estate support almost never needs any courts at all, and if they are not well managed, then they need just and mercy courts about equally (perhaps slightly more mercy), and harsh courts to varying degrees.
My advice would be to learn how to best use each of the three courts, because it's likely you will need to use them all at some point -- especially if you find yourself short on knights and don't have enough estates, like to run your tax rate high, have your region starve, have your region invaded, have a priest stir things up, or become lord of a recently TO'd region. In other words, you will certainly need to use all the courts at some point, so best know how to use them. Luckily it says mostly what they do in the game. But for a more in-depth lesson:
Mercy Courts raise morale, and lower realm control. I haven't kept track of exact numbers, but I'd say . . . a gain of about 9% +/- 4% morale, and every three or so mercy courts, control goes down by one level.
Harsh Courts lower morale and raise control. Usually one court will raise the control level one step, but sometimes it takes two. You lose probably about as much morale as you gain with a mercy court.
Just Courts raise loyalty and have a random effect on morale. About the same effect on loyalty as a mercy court on morale, you randomly lose or gain morale, up to about 4%.
Now, all this means that generally you should not hold mercy or just courts unless morale or loyalty respectively is below 90% (and really, you can wait until it gets down to like 85%), and harsh courts unless control is at Main or lower (and don't feel the need to rush until it gets down to Provence).
Now, a note -- if you try to hold a mercy or just court in a region with very low (below about 30%) morale or loyalty (I don't know if it's both or either), you risk starting a riot that will lower region stats. This chance is extremely high below about 20%, above that but below about 30%, it's chancy but possibly worth the risk. Harsh courts do not have this risk.
Note that all numbers in the post are approximate, and based on memory and experience rather than any sort of study -- I've simply spent quite a lot of time with Lord characters, and at least twice was given regions that were in horrible shape and told to rebuild them, plus having mentored other people through that process.
