What determines the atom or molecule that receives electrons during oxidation?
When a metal like iron is oxidized, each iron atom loses 3 electrons. These electrons are kept by oxygen atoms from the air. The iron atom becomes an ion charged 3+, and the oxygen atom becomes an ion charged 2-. The positive ions still attract negative ions, and they will never separate. Two iron ions and three oxygen ions are necessary to make a new compound which must be not charged. This assembly is a new substance called rust, which has a brown color. Once such a transformation has happened, the next iron atoms can repeat this operation : the amount of rust will slowly increase. 

All metals can be oxidized by more or less the same way. But it could be quicker or longer.  For copper, this reaction is not so frequent. Copper makes a copper oxide which is black, but you may wait for months to see it.