Thomson-Scattering based systems offer a path to high-brightness high-energy (> 1 MeV) x-ray and γ-ray sources due to their favorable scaling with electron energy. LLNL is currently engaged in an effort to optimize such a device, dubbed the "Thomson-Radiated Extreme X-Ray" (T-REX) source, targeting up to 680 keV photon energy. Such a system requires precise design of the interaction between a high-intensity laser pulse and a high-brightness electron beam. Presented here are the optimal design parameters for such an interaction, including factors such as the collision angle, focal spot size, optimal bunch charge, and laser energy. These parameters were chosen based on extensive modelling using PARMELA and in-house, wellbenchmarked scattering simulation codes.