What was the branch of service of in the Vietnam war?

When drafted men were being processed into the US Army, usually in a chartered civilian building; 20 to 30 men would be in a room undergoing one of MANY examinations. A US Marine, with an assistant, with clipboards, would point his pen or finger to certain men within the room and say, "you, you, and you...stand over there!" Minutes would go by, as they wrote data onto their clipboards, they'd look up at the chosen men and say, "you three men are going into the Marine Corps." The US Navy, Air Force, and Coast Guard had a WAITING LIST to join. As did the State National Guards within each state.