Renewable Energy Communities (RECs), supported by the EU Renewable Energy Directive (RED II/III) and national incentives such as those in Italy, are emerging as key enablers of the energy transition by building integrating photovoltaic (BIPV) systems and battery energy storage systems (BESS) at the local level. However, beyond technical and economic optimization, RECs face challenges in investment options, energy trading, and equitable benefit distribution. Existing studies often overlook the diversity of household attributes, leading to potential inequities that undermine participation and long-term viability. This study focuses on two main PV-BESS system investment strategies, community self-invests and a third party invests, developing an Mixed-Integer Linear Programming (MILP)-based Energy Management System (EMS) optimization framework that maximizes community profits while ensuring fairness in individual returns based on various household attributes.