The rapid proliferation of artificial intelligence (AI) models and methods presents growing challenges for research software engineers and researchers who must select, integrate, and maintain appropriate models within complex research workflows. Model selection is often performed in an ad hoc manner, relying on fragmented metadata and individual expertise, which can undermine reproducibility, transparency, and overall research software quality. This work proposes a structured and evidence-driven approach to support AI model selection that aligns with both technical and contextual requirements. We conceptualize AI model selection as a Multi-Criteria Decision-Making (MCDM) problem and introduce an evidence-based decision-support framework that integrates automated data collection pipelines, a structured knowledge graph, and MCDM principles. Following the Design Science Research methodology, the proposed framework (ModelSelect) is empirically validated through 50 real-world case studies and comparative experiments against leading generative AI systems. The evaluation results show that ModelSelect produces reliable, interpretable, and reproducible recommendations that closely align with expert reasoning. Across the case studies, the framework achieved high coverage and strong rationale alignment in both model and library recommendation tasks, performing comparably to generative AI assistants while offering superior traceability and consistency. By framing AI model selection as an MCDM problem, this work establishes a rigorous foundation for transparent and reproducible decision support in research software engineering. The proposed framework provides a scalable and explainable pathway for integrating empirical evidence into AI model recommendation processes, ultimately improving the quality and robustness of research software decision-making.