Final answer:
The Median Cubital vein is the correct vessel to attempt to draw from first when collecting a routine blood sample.
Step-by-step explanation:
The correct vessel to attempt to draw from first when collecting a routine blood sample is the Median Cubital vein. The Median Cubital vein is a superficial vessel located in the antecubital region that links the cephalic vein to the basilic vein in the form of a 'v' shape. It is the most common site for drawing venous blood in humans.