Final answer:
The most economical and safest method for routine venipuncture is the use of evacuated tubes, which are designed for single-use and have an in-built vacuum for accurate blood collection.
Step-by-step explanation:
The most economical and safest method for performing routine venipuncture is the use of evacuated tubes. Unlike butterflies, plastic syringes, or glass syringes, evacuated tubes are designed for a single-use, which minimizes the risk of contamination and ensures accuracy in the blood volume collected. Additionally, evacuated tubes are cost-effective because they are produced in bulk and reduce the time required for the procedure, since they are equipped with a vacuum that pulls the correct amount of blood into the tube, without the need for manual suction.