The suitability of organic Rankine cycle (ORC) technology for the conversion of low- and medium-grade heat sources to useful power has established this as a promising option in geothermal power-generation applications. Despite extensive research in this field, most of which has focused on parametric analyses and thermodynamic performance evaluations, there is still a lack of understanding concerning the comparative performance of different plant configurations from both thermodynamic and economic perspectives. This study seeks to investigate the thermo-economic performance of subcritical and transcritical geothermal ORC power-plants, while considering a range of working fluids and the use of superheating and/or recuperation. A specific case study based on the exploitation of a medium-temperature geothermal heat source (180 °C, 40 kg/s) is conducted. Multi-objective optimization is performed to maximize the power/exergy efficiency (i.e., resource use) and to minimize the payback period. Different optimized configurations are compared and the influence on system performance of superheating, recuperation, and subcritical vs. transcritical operation are evaluated. The results reveal that superheating is preferable for working fluids with low critical temperatures, but hinders the performance of fluids whose critical temperature is higher. Recuperation is not attractive under most operating conditions, since the thermodynamic performance improvement and cooling water saving cannot compensate the cost associated with the installation of the additional heat exchanger. Finally, transcritical ORC systems are favored thanks to the better thermal match between the heat source and the working fluid in these configurations. A more generalized geothermal heat source is then considered to explore the optimal configuration over a range of heat sources, which indicates that non-recuperated transcritical-cycle systems with working fluids whose critical temperature is close to the heat-source temperature are generally favorable.