The objective of this study is to showcase the key geological and reservoir engineering parameters that influence underground hydrogen storage, demonstrate the value of some petrophysical data, and show how hydrogen storage differs between depleted gas fields and saline aquifers for reservoir and geomechanical modeling. We utilized numerical simulation modeling to create a base-case model of a synthetic reservoir that accurately represented the hydrodynamic conditions relevant to underground hydrogen storage in porous media. A two-step sensitivity analysis was then conducted. Firstly, we identified the critical parameters that significantly influence the storage and flow of hydrogen in porous media. Subsequently, we analyzed the geomechanical impact of underground hydrogen storage. In addition, we compared the behavior of hydrogen storage to natural gas storage. The study showed that the reservoir depth or current pressure, the reservoir dip, and the flow capacity were the top three factors impacting the optimal withdrawal of hydrogen. The study also revealed that rock displacement and stress changes were important to be monitored, while changes in strain were not significant. If it is assumed that injection occurs in a critically stressed rock, hydrogen injection and withdrawal in saline aquifers could result in more incidence of microseismicity compared to hydrogen storage in depleted fields or even gas storage in depleted fields. This study quantifies uncertainties in data and pinpoints areas where petrophysical measurements could minimize the uncertainty associated with critical parameters relevant to underground hydrogen storage. It also identifies gaps in measurements for hydrogen storage in porous media. These parameters with large uncertainty are crucial for selecting optimal sites for hydrogen storage and detecting subsurface integrity issues when monitoring for underground hydrogen storage in porous media.