Molten salt reactors (MSRs) are promising advanced nuclear reactors for closure of the fuel cycle. This paper discusses the core design of graphite-moderated MSRs, thanks to a parametric study of the fuel and moderator lattice. The study is conducted at equilibrium of the thorium-uranium fuel cycle for several fuel channel radius and moderator block size combinations. The equilibrium composition for each studied configuration is derived with the help of an in-house MATLAB code, EQL0D, which uses the Serpent 2 Monte Carlo neutronics code for the calculation of reaction rates. The results include excess reactivity at equilibrium, mirroring the breeding gain, and the actinide vector composition for each configuration. Moreover, the occurence of an optimum of the excess reactivity per percent uranium-233 was observed. The investigations showed that it is systematically seen at an interchannel distance equal to the neutron slowing-down length in graphite for each configuration and does not depend on the salt channel radius beyond a certain size, which is given by the thermal fission rate reaching the levels of the fast fission rate. In this way, an exotic energy and spatial distribution of the neutrons are attained. The investigations highlight the potential attractiveness, from a neutronics/fuel cycle point of view, of both large fuel channels and moderators with a shorter neutron slowing-down length.