Different materials and proton beam energies have been studied in order to search for an optimized neutron production target and beam shaping assembly for accelerator-based BNCT. The solution proposed in this work consists of successive stacks of Al, polytetrafluoroethylene, commercially known as Teflon®, and LiF as moderator and neutron absorber, and Pb as reflector. This assembly is easy to build and its cost is relatively low. An exhaustive Monte Carlo simulation study has been performed evaluating the doses delivered to a Snyder model head phantom by a neutron production Li-metal target based on the ⁷Li(p,n)⁷Be reaction for proton bombarding energies of 1.92, 2.0, 2.3 and 2.5 MeV. Three moderator thicknesses have been studied and the figures of merit show the advantage of irradiating with near-resonance-energy protons (2.3 MeV) because of the relatively high neutron yield at this energy, which at the same time keeps the fast neutron healthy tissue dose limited and leads to the lowest treatment times. A moderator of 34 cm length has shown the best performance among the studied cases.