Selecting an enterprise resource planning (ERP) system that simultaneously satisfies sustainability, circular economy, and Industry 4.0 requirements is a multi-criteria decision problem complicated by incomplete information and small expert panels, in which judgments are more naturally expressed as ordinal priorities than as precise scores. To address the lack of an integrated sustainable-ERP (S-ERP) selection framework for these conditions, this study develops and applies a Grey System Theory (GST)–based Grey Ordinal Priority Approach (OPA-G). The framework embeds sustainability, circular economy, and Industry 4.0 criteria in a single decision structure and represents the judgments of a three-member expert panel as ordinal priorities under grey interval uncertainty, avoiding pairwise comparisons while preserving uncertainty through grey numbers. The model is applied to a real manufacturing case, and its robustness is tested through seven expert-priority scenarios together with area-level (±10%, ±20%) and ordinal perturbation analyses, and benchmarked against Grey TOPSIS and Grey VIKOR. The results show that the Fundamental and Economic criteria dominate the decision (0.640), followed by Industry 4.0 compatibility (0.233), environmental (0.099), and social (0.028) criteria; System Cost, Quality, and Financial Situation are the most influential criteria, while Cloud and Edge Computing, Artificial Intelligence, and IoT are the leading digital requirements. The framework yields the ranking ERP1 > ERP2 > ERP3 > ERP4, which remains unchanged across all perturbation scenarios and is reproduced identically by Grey TOPSIS and Grey VIKOR. Although economic performance remains primary, Industry 4.0 capabilities are the decisive enablers that make environmental and social monitoring operationally executable. The proposed framework therefore offers a transparent, robust, and practically implementable decision-support tool for sustainable ERP procurement under uncertainty, extensible to multi-firm panels and broader sustainability domains.