Point cloud quality assessment (PCQA) has advanced significantly with synthetic datasets offering diverse distortion coverage for model training. However, when applied to new application scenarios, models often suffer from performance drops due to mismatched distortion characteristics between source and target domains. Most current methods use all available synthetic distortions, which may introduce irrelevant features and hinder generalization. To address this, we propose DST-PCQA, a distortion-selective training framework for PCQA. Unlike previous approaches that treat all distortions equally, DST-PCQA identifies and selects distortion types most relevant to a target domain by analyzing inter-domain distortion similarity. This selective strategy reduces negative transfer and enables efficient domain-specific training. To fully leverage the selected distortions for both classification and quality prediction, we adopt a dual-branch architecture that fuses 2D visual cues and 3D geometric structure via cross-modal attention. This design supports multi-level feature alignment across modalities and enables fine-grained distortion understanding. Extensive evaluations across three target domains have verified the effectiveness of DST-PCQA over full-set training baselines. Moreover, its distortion-selective strategy is orthogonal to existing model-based PCQA methods, enabling improved cross-domain performance and reduced training costs across a wide range of architectures.