Deep recommender systems (DRS) often face challenges in balancing computational efficiency and model accuracy, especially when handling high-dimensional input features. Existing methods either focus on improving accuracy while neglecting training efficiency or prioritize efficiency at the cost of suboptimal accuracy across tasks. We propose Light-FMP: Lightweight Feature and Model Pruning for Enhanced DRS, a lightweight framework that addresses the challenges through three key phases: \textit{pretraining}, \textit{pruning}, and \textit{continued training}. Using a hard concrete distribution, a masking layer is efficiently pretrained on a small data subset to identify important features. The model and features are then pruned, and training continues on the remaining dataset with domain-adapted parameters. Experiments on benchmark datasets from real-world recommender systems demonstrate that Light-FMP outperforms existing methods in both efficiency and accuracy while maintaining scalability and robustness.