Final answer:
When collecting a routine blood sample, the phlebotomy technician should attempt to draw from the median cubital vein first.
Step-by-step explanation:
The phlebotomy technician should attempt to draw blood from the median cubital vein first when collecting a routine blood sample. The median cubital vein is the most common site for drawing venous blood in humans. It is located in the antecubital region of the arm, where it crosses at an angle to join the cephalic vein.