The phenomenological and microscopic level density models were utilized within the TALYS 2.0 software to simulate the cross-sections of proton-induced reactions on both natural and enriched copper. This process resulted in the production of the zinc radioisotopes 62Zn, 63Zn, and 65Zn, which hold significance in diagnostic and therapeutic medicine. We assessed the uncertainty values for all computed cross sections by contrasting them with experimental data taken from the EXFOR database. This was undertaken to deliver a thorough and precise account of the predictions across various incident energy, grounded in the relevant uncertainty values associated with each energy value. We calculated the average uncertainty through the relative variance technique to identify the theoretical model that aligns most closely with the experimental data. The simulations demonstrated high accuracy when employing level density models, particularly the Skyrme-Hartree-Fock-Bogolyubov-Goriely's tables (SHFB) model, which exhibited excellent relative variance values for the majority of the reactions analyzed. Furthermore, specific energy values linked to significant uncertainty were recognized, indicating the necessity to steer clear of these energies in upcoming investigations aimed at producing 62,63,65Zn radioisotopes. The theoretical yield was determined by utilizing the cross-section results derived from the most accurate model for each reaction, followed by a comparison with the experimental values. The majority of the chosen experimental yield values demonstrated strong consistency. The findings suggest that the yield for proton-induced reactions on enriched copper exceeded that of natural copper. Furthermore, the generation of zinc isotopes does not necessitate elevated incident energy, rendering these reactions particularly appropriate for application with small medical cyclotrons.