In light of escalating global energy demands and the imperative to reduce greenhouse gas emissions, the efficient transportation of liquefied natural gas (LNG) has become increasingly critical. As the evaporation of LNG from storage tanks represents a significant energy loss, improving tank insulation is crucial to optimize storage efficiency. This paper conducts a structural assessment of a smaller-sized Type C independent tank made of AISI 304L steel and examines the impact of two insulation techniques—vacuum and perlite—on their heat, structural, and fatigue behavior. Utilizing the finite element method (FEM), this study performs a heat transfer analysis followed by a structural analysis under combined loads in accordance with the International Gas Carrier (IGC) code. The subsequent fatigue analysis follows IGC procedures and is performed using third-party software. This article presents a detailed analysis of the heat transfer throughout the entire LNG tank and the stress levels under various combined load scenarios while providing insights into the critical stress points and the areas with the lowest fatigue life. Finally, this study confirms the viability of using both novel materials, perlite as an insulation material and Durolight for the tank support, because they meet the required limits.