The building sector's impacts on climate are widely acknowledged, leading to policies and standards promoting energy-efficient buildings. In order to achieve sustainability in a holistic sense, the environmental, social, and economic impacts of equipment used in buildings need to be evaluated. In this regard, a novel decision support framework is introduced to evaluate the heating and cooling equipment in single-family detached homes. Energy simulation, life cycle environmental, social, and economic analyses, and a multi-criteria decision-making method are used to identify the most sustainable set of equipment. This framework is demonstrated through its application on mechanical and water heating equipment in three existing residential buildings of varying energy efficiencies (low, medium, and high, the latter being net-zero-ready) over a 50-year study period.The results indicate that the carbon footprint of a natural gas furnace is six times higher than that of other equipment. Across various lifecycle phases, the product stage accounts for more than 50% of the total impacts for most equipment. In contrast, the drain water heat recovery unit shows the lowest impacts attributed to its lower materials and energy usage. When grouped, the equipment in the low-efficiency home showed the highest endpoint impacts, while the equipment in the medium-efficiency home had higher social and economic impacts. Overall, the equipment set in a net-zero home is the best choice under equal, pro-social, and pro-economic weight scenarios and only lags behind the equipment set in a medium-efficiency home for pro-environmental scenarios. The work will help improve sustainable building policies beyond immediate energy and cost savings.