Porosity and permeability are crucial indicators in the identification of high-quality reservoirs and favorable “sweet spot” zones, as well as key parameters when predicting and evaluating the development potential of fossil fuels like oil and gas. However, it is impracticable to collect enough core samples on vertical and horizontal planes for analysis due to the associated time and cost demand. Machine learning algorithms have shown remarkable capabilities in predicting the petrophysical properties by capturing non-linear relationships among logging data. In this study, to quantify the selection of logging curves and reduce the redundant logging data input, a novel and interpretable Permutation Importance-Set algorithm is proposed on the basis of logging data from the Upper Triassic Xujiahe Formation in the Sichuan Basin. The results indicate that, because of compaction, burial depth is the primary feature affecting the physical properties of tight sandstone reservoirs. Acoustic and spontaneous potential logs are critical for porosity, while density and spontaneous potential logs are pivotal for permeability, reflecting the complex diagenesis caused by the widespread sand-mud interbedding. Basin-level prediction models for porosity and permeability were developed using ten machine learning algorithms, then ablation studies confirmed the effectiveness of our feature selection and the reduced model complexity and over-fitting. This study offers a concise, interpretable prediction model with superior accuracy and interpretability for tight sandstone reservoirs.