  Recent experiments have established that semiconductor-based moir\'e
materials can host incompressible states at a series of fractional
moir\'e-miniband fillings. These states have been identified as generalized
Wigner crystals in which electrons localize on a subset of the available
triangular-lattice moir\'e superlattice sites. In this article, we use
momentum-space exact diagonalization to investigate the many-body ground state
evolution at rational fillings from the weak-hopping classical lattice gas
limit, in which only spin degrees-of-freedom are active at low energies, to the
strong-hopping metallic regime where the Wigner crystals melt. We specifically
address the nature of the magnetic ground states of the generalized Wigner
crystals at fillings $\nu$ = 1/3 and $\nu$ = 2/3.
