The application of the fused deposition modeling (FDM) additive manufacturing process has increased in the production of functional parts across all industries. FDM is also being introduced for industrial tooling and fixture applications due to its capabilities in building free-form and complex shapes that are otherwise challenging to manufacture by conventional methods. However, there is not yet a comprehensive understanding of how the FDM process parameters impact the mechanical behavior of engineered products, energy consumption, and other physical properties for different material stocks. Acquiring this information is quite a complex task, given the large variety of possible combinations of materials–additive manufacturing machines–slicing software process parameters. In this study, the knowledge gap is filled by using the Taguchi L27 orthogonal array design of experiments to evaluate the impact of five notable FDM process parameters: infill density, infill pattern, layer thickness, print speed, and shell thickness on energy consumption, production time, part weight, dimensional accuracy, hardness, and tensile strength. Signal-to-noise (S/N) ratio analysis and analysis of variance (ANOVA) were performed on the experimental data to quantify the parameters’ main effects on the responses and establish an optimal combination for the FDM process. The novelty of this work is the simultaneous evaluation of the effects of the FDM process parameters on the quality performances because most studies have considered one or two of the performances alone. The study opens an opportunity for multiobjective function optimization of the FDM process that can be used to effectively minimize resource consumption and production time while maximizing the mechanical and physical characteristics to fit the design requirements of FDM-manufactured products.