We perform a systematic analysis of the relationship between the molecular geometry, the force-field parameters, the magnitude of the induced dipoles, and the resulting site-site microstructure of a model for water consisting of simple point charges plus a self-consistent point dipole polarizability. We constrain the model to represent the experimental values of the pressure and the configurational internal energy of water at ambient conditions, while keeping a permanent dipole moment of 1.85 D. The resulting force fields are then used to perform additional simulations at high temperature to determine the effect of polarizabilities on the site-site structure, and to make contact with neutron scattering experiments as well as ab initio simulation results. We show that the parameterization of the model is possible for 0 less than or equal to R(OM)less than or equal to 0.25 Angstrom, where R(OM) is the oxygen-to-negative charge distance along the bisectrix of the H-O-H angle, resulting in total dipole moments from 2.88 to 3.03 D, with polarization energies accounting for 40%-57% of the total configuration internal energy of water. These results, in conjunction with the behavior of the short range site-site correlation functions, highlight the shortcomings of the simple point charge approximation for the polarization behavior at short intermolecular distances, and give a meaningful reference from which we can attempt to overcome these defects.