Hyperspectral image (HSI) and SAR/LiDAR data offer complementary spectral and structural information for land-cover classification. However, their effective fusion remains challenging due to two major limitations: The spectral redundancy in high-dimensional HSI and the heterogeneous characteristics between multi-source data. To this end, we propose Representative Spectral Correlation Network (RSCNet), a novel multi-source image classification framework specifically designed to address the above challenges through spectral selection and adaptive interaction. The network incorporates two key components: (1) Key Band Selection Module (KBSM) that adaptively selects task-relevant spectral bands from the original HSI under cross-source guidance, thereby alleviating redundancy and mitigating information loss from conventional PCA-based spectral reduction. Moreover, the learned band subset exhibits highly discriminative spectral structures that align with discriminative semantic cues, promoting compact yet expressive representations. (2) Cross-source Adaptive Fusion Module (CAFM) that performs cross-source attention weighting and local-global contextual refinement to enhance cross-source feature interaction. Experiments on three public benchmark datasets demonstrate that our RSCNet achieves superior performance compared with state-of-the-art methods, while maintaining substantially lower computational complexity. Our codes are publicly available at https://github.com/oucailab/RSCNet.