Generating effective query suggestions in conversational search requires aligning model outputs with user preferences, which is challenging due to sparse and noisy click signals. We propose GQS, a generative framework that integrates click modeling and preference optimization to enhance real-world user engagement. GQS consists of three key components: (1) a Multi-Source CTR Modeling module that captures diverse contextual signals to estimate fine-grained click-through rates; (2) a Diversity-Aware Preference Alignment strategy using CTR-weighted Direct Preference Optimization (DPO), which balances relevance and semantic diversity; and (3) a CTR-Calibrated Iterative Optimization process that jointly refines the CTR and generation models across training rounds. Experiments on two real-world tasks demonstrate that GQS outperforms strong baselines in CTR, relevance, and diversity.