Each voice has it's own quality and personality. And each of us drives our voice differently which is why we have different issues.
For example, a singer who is suffering from voice strain after a performance definitely has problems with the breath support. No way around that.
A singer who has a weak head voice could be singing too much in the chest voice which will cause an overall imbalance from which springs a multitude of other problems.
So we need to work with exercises that won't interfere with our voices' need to develop at it's own healthy rate, or cause mistakes to get worse. To me this means starting with exercises that are easy. Let strengths develop and eventually correct mistakes.
If you want to strengthen the natural breath support, do exercises that challenge the breathing. Singing through an exercise pattern and having the goal to make it sound beautiful and easy to the last note should be the goal. If you keep your mind focussed on this, your body will take care of the rest.
If you're working with an exercise and it's giving you trouble or strain, then definitely stop doing it. It could be that your voice wasn't warm enough for the task. Or you might need to take a step down to something easier and practice that for a while. After a while (how long is up to you) try the harder exercise.