As a newly trained fitness instructor, what is important for me to do or take (vitamin)to avoid over straining my body & how do I best look after it?

Use good sense. The best way to avoid over straining your body is to not over strain your body. Keep yourself well nourished with healthy foods. Get good sleep and be consistent in sleep habits. And when your body tells you that you are too fatigued or you begin to feel pain, that's a huge red flag that you're over straining and you need to back off and rest a bit. Vitamins don't prevent over straining.
No. Vitamins won't allow you to avoid straining or improve your appearance after training. Those goals are laudable but aren't necessarily dependent upon them. That being said, taking a daily multivitamin and some essential minerals are important for overall good health and specifically in the context of vigorous exercise.