Hyperspectral Image (HSI) processing stands at the forefront of remote sensing technologies, offering a wealth of detailed information crucial for various environmental and agricultural applications. The complexity of HSI datasets demands sophisticated techniques for accurate and efficient analysis. In this research, we investigate the efficiency of feature selection and extraction methods for HSI classification using Fast-3D Convolutional Neural Networks (CNN) and Residual Neural Networks (ResNet). Our motivation stems from the necessity to enhance accuracy and computational efficiency in remote sensing applications. We conducted experiments on two prominent HSI datasets, Indian Pines and Salinas, leveraging feature selection techniques like Correlation-based Feature Selection (CFS), Mutual Information Feature Selection (MIFS), Linear Discriminant Analysis (LDA), and Recursive Feature Elimination (RFE), alongside feature extraction methods such as Principal Component Analysis (PCA), Incremental PCA (IPCA), Quadratic Discriminant Analysis (QDA), and Non-negative Matrix Factorization (NMF), implemented within both Fast-3D CNN and ResNet architectures. Our results indicate that in hyperspectral data classification for both Indian Pines and Salinas datasets, IPCA and QDA excelled in accuracy (99.68%, 99.14%) within the Fast-3D CNN architecture, with IPCA demonstrating speed (0.40 s, 1.40 s). CFS displayed notable efficiency (99.27%, 90.88%) with minimal processing time (0.56 s, 1.35 s) in the Fast-3D CNN architecture. RFE achieved high accuracy (99.88%, 96.39%) with reasonable processing times (2.28 s, 11.53 s) in the ResNet architecture. While IPCA led in extraction (99.90%, 99.12%), it required more time (21.17 s, 2.23 s) in the ResNet architecture. These results underscore the practical significance of feature extraction methods like IPCA for accuracy-focused tasks and the efficiency of feature selection methods like CFS in scenarios prioritizing computational time.