The development of hybrid renewable systems is an economically competitive solution to reach energy decarbonization and reduction of greenhouse gasses. Based on the literature, energy, economic and environmental indicators were rarely simultaneously employed in the optimization of a hybrid renewable system. In addition, there is no procedures or a set of indicators to be applied uniformly in all applications for the shared analysis. The paper presents a novel energy-economic-environmental multi-criteria decision-making in the optimization of a hybrid renewable system, based on a new set of dimensionless indicators, proposed as a standard for future applications. The procedure compares the entire PV-wind-battery system configuration with the PV-wind, PV-battery and wind-battery system sub-configurations. A width parametric and multi-optimization analysis permit the identification of the most proper nominal powers of each system component. The procedure proposed was applied in a Mediterranean residential building, demonstrating that some system configurations allow complying simultaneously with at least two of the three energy objectives proposed, the cost-optimal level and the maximum reduction of emissions, for specific values of the load. The solar source was the most suitable both from energy, environmental and economic point of view, while the use of the wind source leads to a greater system operating time in the nominal power conditions. The study pointed out and quantified that, for specific loads, PV, wind and battery powers, the development of specific incentives for wind systems and of battery systems with a higher lifespan can help to make the hybrid systems more economically competitive.