The following are the main systemized ways to set exercise order.
If you want to train wisely, you set the exercise order of your workout by giving priority to the exercises that demand the most amount of neural stimulus. Which is why compound exercises such as the squat, deadlift, and clean are usually performed first in a workout.
It is also common to give priority to what you want to improve the most. By performing an exercise early in your workout when you are fresh, you can apply the most amount of intensity. For the same reason, priority is also usually given to weaknesses.
Stacking is where you repeat the same exercise, or exercises of the same muscle group, one after the other.
Paired set training is where you alternate between two exercises of opposing agonist and antagonist muscle groups. Rest times are typically shorter being 2 minutes or less. One of the main advantages is time saving. It allows the targeted muscle groups to recover while you perform the alternate exercise.
Another advantage of this system is that it keeps a high metabolic rate for those wanting to lose body fat.