Laser-accelerated protons, generated by irradiating a solid target with a short, energetic laser pulse at high intensity (I > 1018 W·cm−2), represent a complementary if not outperforming source compared to conventional accelerators, due to their intrinsic features, such as high beam charge and short bunch duration. However, the broadband energy spectrum of these proton sources is a bottleneck that precludes their use in applications requiring a more reduced energy spread. Consequently, in recent times strong effort has been put to overcome these limits and to develop laser-driven proton beamlines with low energy spread. In this paper, we report on beam dynamics simulations aiming at optimizing a laser-driven beamline - i.e. a laser-based proton source coupled to conventional magnetic beam manipulation devices - producing protons with a reduced energy spread, usable for applications. The energy range of investigation goes from 2 to 20 MeV, i.e. the typical proton energies that can be routinely obtained using commercial TW-power class laser systems. Our beamline design is capable of reducing the energy spread below 20%, still keeping the overall transmission efficiency around 1% and producing a proton spot-size in the range of 10 mm2. We briefly discuss the results in the context of applications in the domain of Cultural Heritage.