Accurate International Classification of Diseases (ICD) coding is critical for clinical documentation, billing, and healthcare analytics, yet it remains a labour-intensive and error-prone task. Although large language models (LLMs) show promise in automating ICD coding, their challenges in base model selection, input contextualization, and training data redundancy limit their effectiveness. We propose a modular framework for ICD-10 Clinical Modification (ICD-10-CM) code prediction that addresses these challenges through principled model selection, redundancy-aware data sampling, and structured input design. The framework integrates an LLM-as-judge evaluation protocol with Plackett-Luce aggregation to assess and rank open-source LLMs based on their intrinsic comprehension of ICD-10-CM code definitions. We introduced embedding-based similarity measures, a redundancy-aware sampling strategy to remove semantically duplicated discharge summaries. We leverage structured discharge summaries from Taiwanese hospitals to evaluate contextual effects and examine section-wise content inclusion under universal and section-specific modelling paradigms. Experiments across two institutional datasets demonstrate that the selected base model after fine-tuning consistently outperforms baseline LLMs in internal and external evaluations. Incorporating more clinical sections consistently improves prediction performance. This study uses open-source LLMs to establish a practical and principled approach to ICD-10-CM code prediction. The proposed framework provides a scalable, institution-ready solution for real-world deployment of automated medical coding systems by combining informed model selection, efficient data refinement, and context-aware prompting.