The first rock expected to crystallize is Olivine. Olivine is a silicate mineral that is green in colour. Fractional crystallization is the process by which the crystals formed in a cooling magma are segregated from the remaining liquid.
The Bowen's reaction series provides a model to show that as magma temperature decreases olivine and other minerals crystallize in a particular order. As magma cools, minerals crystallize at different temperatures and settle out of the magma.