We propose a hybrid depression detection framework that combines classical feature selection with self-supervised speech representations, evaluated on the Androids dataset, which includes Reading and Interview Tasks. We extract low-level OpenSMILE descriptors and apply Recursive Feature Elimination (RFE) across five classifiers. Majority voting identifies a stable 15-feature subset, which feeds an ensemble of Support Vector Machine (SVM), Random Forest (RF), Extreme Gradient Boosting (XGBoost), and a small neural network. This setup yields 86.9% accuracy and 80.0% F1-score, improving the SVM-only baseline by 13.6 and 6.4% points, respectively. In addition, we use a frozen WavLM-Base-Plus encoder to generate contextual embeddings, aggregated by an eight-head self-attention layer and a two-layer MLP. This model achieves 89.2% precision on the Reading Task and 97.4% on the Interview Task, outperforming a frame-wise LSTM baseline by 5 and 13% points. Our results highlight the complementary strengths of targeted feature selection and global context-aware representations, forming a robust framework for detecting depression from speech.