Hydrogen (H2) emerges as a pivotal player in the transition to renewable energy sources. To address the seasonal fluctuations in energy dynamics, underground storage emerges as the most efficient approach, and saline aquifers within sedimentary basins as promising repositories for substantial H2 volumes. However, this potential storage solution remains relatively unexplored. Conducting a comprehensive health, safety, and environment (HSE) risk assessment is vital for the technological advancement and public acceptance of geological H2 storage sites. This study introduces a methodology designed to select and classify potential formations based on their HSE risks, offering a safety-oriented approach to identifying suitable storage sites. The proposed methodology underwent testing in two deep saline aquifers located in distinct geological contexts within the Iberian Peninsula. The aim of this study is to establish a foundation for further investigations and implementation of geological H2 storage sites while ensuring safety and adhering to environmental and health standards.