We simulate on the computer the kinetics of structure formation upon quenching a polymer solution inside a two-phase region. Our description is on a mesoscopic scale, and the polymer is represented by a chain of beads on a cubic lattice. The results presented are for a 10% solution of polyethylene with a monodisperse molecular weight M = 140 000. We find that the polymer structure grows in two stages. In the first stage, a bicontinuous percolated microstructure is formed through spinodal decomposition and the sizes of the phase domains increase linearly with time. Within that stage, deep quenches lead to lacy structures made of fine and dense fibrils, whereas shallow quenches form wide ribbons with many voids. At the percolation-to-cluster transition, a second stage occurs in which the polymer network breaks into isolated aggregates by diffusive coarsening and sizes grow more slowly as R-4 similar to Kt.