Fastest distribution of some injected materials/medicines & with no risk of any kind can be achieved by injecting it into - artery or vein?
It depends on what your target tissue is, as @another 'Homo sapien' stated.
If you want to get something to the hand, for instance, injecting it into the brachial artery will get it there "faster" than injecting it into the cephalic vein.
Fastest distribution of some injected materials/medicines & with no risk of any kind
does not exist. There are risks with any invasive proceedure, and invading arteries is riskier than invading veins. Unless the risk outweighs the benefit, substances which cannot be administered orally are given intravenously. Arterial lines are usually used for purposes other than injecting substances.