Q
"What is the best brace height for my bow?"
A
It depends on the type of bow and the manufacturer. You should check the manufacturer's guidelines for the best brace height. If you cannot find the manufacturer's guidelines for the ideal brace height then you may need to experiment a bit.
Once you have the manufacturer's recommended distance then you just measure the distance between the lowest point in the handle to the bowstring. If it is too low you need to tighten the string by twisting it about 5 to 10. If the bow string is too high then you need to untwist it 5 or 10 times and check again. Keep repeating this process until you reach the optimal distance.
I personally use the "rule of thumb" method for recurve bows, and slightly less than that for longbows and flatbows. I am less worried about being exactly precise because I know the optimal brace height is really often a range within 1 to 2 inches of the rule of thumb method.
The important things to keep in mind are the physics involved...
The Physics of Brace Height
Too Long Bow String = Too Low Brace Height = Bow string de-accelerates, causing slower arrows, more arrow vibration, more bow vibration, sluggish accuracy.
Perfect String Length = Optimum Brace Height = Bow string accelerates fully, causing nice fast arrows, reduced vibrations, optimal accuracy.
Too Short Bow String = Too High Brace Height = Bow string doesn't accelerate fully, causing slower arrows, vibrations are still reduced, accuracy is down because arrow speed is slower.
Optimal > Too High > Too Low.
Thus it is better to be slightly too high than slightly too low, but ideally you want to get as close to the Optimal Brace Height as you can.
So if you cannot find the manufacturer's recommended brace height then it is better to try the "rule of thumb method" and experiment a bit.
If your bow string is hitting you in the wrist during shots then your brace height is definitely too low.
What is the rule of thumb method?
Holding the bow sideways with the string away from you place your hand on the lowest point on the bow's handle in the "thumbs up" position towards the bowstring. If your thumb is touching the bow string then the brace height is too low and is likely to hit you in the wrist.
You then unstring the bow, twist the bow string 10 times to make it tighter, and restring the bow.
You check the brace height again using the rule of thumb method and if it is still touching your thumb then you repeat the process.
Because people have different sizes of hands the optimal brace height may be roughly 1 or 2 inches above your thumb.
Notes
With longbows and flatbows expect the optimal brace height to be slightly lower than what is normal for recurves, so closer to your thumb or even touching your thumb.
If a bow string is brand new expect it to stretch a bit during the first hour of being used. You may need to stop and adjust the bow string's brace height 30 to 45 minutes a second time.