In this paper we describe a model for a fully numerical Monte Carlo simulator and the required inputs, which include the calculation of numerical phonon scattering rates and the electronic bandstructure. The model is material-independent, and it therefore provides great flexibility in the ability to characterize many semiconductor materials, including the III-V and III-Nitride materials. All of the principal ingredients of the Monte Carlo model are determined numerically from first principles with one exception, that of the acoustic deformation potential. The determination of the acoustic deformation potential, which specifies the relative strength of the acoustic phonon scattering rate, affects the calculated results. We introduce a methodical approach for its selection and examine the sensitivity of the primary calculated transport quantities on its magnitude. Specifically, we examine how the choice of the acoustic deformation potential, in a completely numerical Monte Carlo model, affects the calculated velocity field curve, average energy, and impact ionization coefficients. Calculations are made for both bulk GaAs and 3C-SiC and for a representative GaAs MESFET structure. It is found that the acoustic deformation potential needs to be energy dependent and that it requires at least two values, one for intra-band transitions and one for inter-band transitions. It is further found that through the use of the fully numerical model introduced here, reliable transport-related results may be obtained for bulk material as well as representative devices using only the acoustic deformation potential as the single adjustable parameter.