The variability of the material properties of steel from different suppliers causes problems in achieving the required surface quality after turning. Therefore, the manufacturer needs to estimate the resulting quality before starting production, especially if it is an expensive, small-batch production from stainless steel. Predictive models will make it possible to estimate the surface roughness from the mechanical properties of steel and thus support decision making about supplier selection or acceptance of a material supply. This research presents a step-by-step decision-making procedure, which enables the trained staff to make quick decisions based on commonly available information in the Mill Test Certificate (MTC). A new multivariate second-order polynomial model and feedforward backpropagation artificial neural network (ANN) models have been developed using input variables from the MTC: Tensile Strength, Yield Strength, Elongation, and Hardness. Models were used to enhance the methodological robustness in formulating the decision if the predicted surface roughness is outside the required range, even before accepting the delivery. Both models can accurately predict surface roughness, while the ANN model is more accurate than the polynomial model; however, the predictive model is sensitive to the accuracy of the input data, and the model’s prediction is valid only under precisely defined conditions.