Summary: This work examines the Grundy chromatic number (First-Fit chromatic number) of comb product graphs constructed from standard graph classes such as paths, cycles, and complete graphs. Exact values are derived for combinations including \(P_q\circ P_{q'}\), \(P_q\circ K_t\), \(K_t\circ K_t'\), \(C_r\circ C_{r'}\), and \(C_r\circ P_q\). The results highlight how base graph interactions impact greedy coloring strategies.