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The earliest I could find was Roman: the Civic crown was a coronet of oak leaves, given for saving the life of a fellow citizen in battle. Julius Caesar won one during the siege of Mytilene. The Civic Crown ranked second highest, after the Grass Crown.
Oaks and their leaves were important for the Celts and later the Germanic tribes as well, culminating much later in military decorations with oak leaves. The earliest modern military decoration is the LΓ©gion d'honneur in 1802. Before that commanders were given noble ranks or knightly decorations, and lower ranks usually a monetary reward. (The grand cross has a laurel and an oak wreath behind the cross.)
The American tradition is merely a continuation of this ancient custom.
Your second question was about the silver/gold insignia difference in the US Army. Wikipedia has a comprehensive explanation on that. In a nutshell: the senior/oldest ranks were silver, and kept it. Junior/newer ranks got gold. Do mind that this is strictly about the US Army. Other armies have different traditions.