Solar energy is a sustainable source that can be effectively utilized to address winter heating challenges in buildings. To ensure the efficient application of solar energy for heating purposes and to maintain reliable performance of the heating system, the integration of phase-change materials (PCMs) in thermal energy storage (TES) systems has emerged as a crucial auxiliary approach. This study focuses on the design and simulation of four TES structures: smooth, finned, metallic foam, and metallic foam-finned tubes. It explores their thermal characteristics, such as complete melting time and heat flux, under various flow conditions. Additionally, a residential building in Xi’an is selected as the object, where the proposed solar energy phase-change TES system is employed to meet the heating demand. Economic indicators, including initial investment and investment payback period, are estimated using a static evaluation method. The results highlight that the complete melting time of the TES unit with a metallic foam-finned tube is 4800 s, which is 88.3% less than the smooth tube. Finally, based on the actual project, it is determined that the metallic foam-finned heating system, with an HTF flow rate of 0.25 m/s, requires the fewest TES devices (914) and has a payback period of 13 months.