Supervised Fine-Tuning (SFT) of the language backbone plays a pivotal role in adapting Vision-Language Models (VLMs) to specialized domains such as medical reasoning. However, existing SFT practices often rely on unfiltered textual datasets that contain redundant and low-quality samples, leading to substantial computational costs and suboptimal performance in complex clinical scenarios. Although existing methods attempt to alleviate this problem by selecting data based on sample difficulty, defined by knowledge and reasoning complexity, they overlook each sample's optimization utility reflected in its gradient. Interestingly, we find that gradient-based influence alone favors easy-to-optimize samples that cause large parameter shifts but lack deep reasoning chains, while difficulty alone selects noisy or overly complex textual cases that fail to guide stable optimization. Based on this observation, we propose a data selection strategy, Difficulty-Influence Quadrant (DIQ), which prioritizes samples in the "high-difficulty-high-influence" quadrant to balance complex clinical reasoning with substantial gradient influence. This enables efficient medical reasoning for VLMs with minimal fine-tuning data. Furthermore, Human and LLM-as-a-judge evaluations show that DIQ-selected subsets demonstrate higher data quality and generate clinical reasoning that is more aligned with expert practices in differential diagnosis, safety check, and evidence citation, as DIQ emphasizes samples that foster expert-like reasoning patterns. Extensive experiments on medical reasoning benchmarks demonstrate that DIQ enables VLM backbones fine-tuned on only 1% of selected data to match full-dataset performance, while using 10% consistently outperforms baseline methods, highlighting the superiority of principled data selection over brute-force scaling. The code is available at https://github.com/mihara-bot/DIQ.