Dynamic contact and impact problems are widely applicable. An accurate solution method for these kinds of problems can be used in many fields of mechanical engineering (e.g., cutting metalwork, cogwheel drives, etc.). However, the proper handling of the contact is problematic, as there emerges a substantial amount of nonlinearity in the displacement field. Therefore, a spurious high frequency oscillation is present in the solution. These oscillations must be avoided, as divergence can easily occur in the contact algorithm due to them. In order to eliminate this effect, the applied numerical method must be chosen and set properly. In this study, a comprehensive guide is provided for the appropriate selection of the proper numerical method and its parameters.