I saw a video recently from a trainer and they recommended focusing on whichever muscles are feeling the most tension that day.
My stretch will involve relaxing the tension from my back. I do this by touching my toes while releasing the tension from my right and lower back
If we look at the body, every part is unique. Each has their own unique functionality but each unique body part can't fully operate certain task, take for instance lifting up a box you need to lift with your legs, you need your back to balance yourself and you need your arms and hands to have a grip over the box. So my personal opinion you need to stretch your whole body just for in case you need to perform certain task.