Polyethylene Terephthalate Glycol (PETG) is a fused deposition modeling (FDM)-compatible material gaining popularity due to its high strength and durability, lower shrinkage with less warping, better recyclability and safer and easier printing. FDM, however, suffers from the drawbacks of limited dimensional accuracy and a poor surface finish. This study describes a first effort to identify printing settings that will overcome these limitations for PETG printing. It aims to understand the influence of print speed, layer thickness, extrusion temperature and raster width on the dimensional errors and surface finish of FDM-printed PETG parts and perform multi-objective parametric optimization to identify optimal settings for high-quality printing. The experiments were performed as per the central composite rotatable design and statistical models were developed using response surface methodology (RSM), whose adequacy was verified using the analysis of variance (ANOVA) technique. Adaptive neuro fuzzy inference system (ANFIS) models were also developed for response prediction, having a root mean square error of not more than 0.83. For the minimization of surface roughness and dimensional errors, multi-objective optimization using a hybrid RSM and NSGA-II algorithm suggested the following optimal input parameters: print speed = 50 mm/s, layer thickness = 0.1 mm, extrusion temperature = 230 °C and raster width = 0.6 mm. After experimental validation, the predictive performance of the ANFIS (mean percentage error of 9.33%) was found to be superior to that of RSM (mean percentage error of 12.31%).