For printing equipment manufacturing enterprises, the selection of an enterprise resource planning (ERP) system involves multiple factors, including function matching degree, technical performance, cost-effectiveness, and others. Therefore, ERP system selection becomes a complex multi-criteria decision-making (MCDM) problem. In this study, a method for ERP system selection suitable for printing equipment manufacturing enterprises is proposed. First, a set of evaluation criteria covering five dimensions—functionality, technicality, implementability, economy, and reputation—is established through literature review. Second, the Fuzzy Analytical Hierarchy Process (FAHP) is used to determine the weights of the evaluation criteria. Then, the gray relational analysis (GRA)-enhanced Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) method is applied to rank the alternatives. Finally, a dual verification mechanism combining weight perturbation and parameter sensitivity is designed to test the robustness of the ranking results. Experimental results show that Alternative 2 is the best ERP system. Furthermore, key evaluation criteria, such as core functionality coverage and purchase price, are considered to be relatively important. The study demonstrates that this model, through methodological innovation and verification mechanism design, effectively integrates subjective and objective information. It provides a solution that is both scientifically sound and practically applicable for ERP system selection in printing equipment manufacturing enterprises.