Which of these methods would be most effective in allowing someone to precisely gauge the intensity level of his exercise

You didn't provide us with any possible answers but if this is the list that you meant:
Complete the talk test
Ask a coach 
Take his pulse
Monitor his water intake

Then the correct answer would be C - take his pulse. 

Doing this, he would able to witness and explore what kind of stress did he put his body under.

Well if you pick a machine to work on and that's gonna be your exercise if you don't stick to that machine your muscle strength your muscle mass rather will change because you haven't been doing it you change something in your exercise routine which changes your body's form of dealing with things for example you might become weaker or stronger depending on what kind of exercises you do in whether or not the machine you picked actually your muscles grow.

The answer is epidermis