Solar-hydrogen generation represents a promising alternative to fossil fuels for the large-scale implementation of a clean-fuel transportation infrastructure. A significant amount of research resources has been allocated to the development of photoelectrochemical components (i.e. photovoltaic and water splitting catalysts) that are able to spontaneously split water in the presence of solar irradiation, which has led to major advances in the solar-fuels field. At the same time, only limited attention has been given to understanding the key aspects that drive economically viable solar-fuel generators. This study presents a generalized approach to understand the economic factors behind the design of solar-hydrogen generators composed of photovoltaic components integrated with water electrolyzers. It evaluates the underpinning effects of the material selection for the light absorption and water splitting components on the cost of the generated fuel ($ per Kg of H-2). The results presented in this work provide insights into important engineering aspects related to the sizing of devices and the use of light concentration components that, when optimized, can lead to costs below $2.90 per kilogram of hydrogen after compression and distribution. Most significantly, the analysis demonstrates that the cost of hydrogen is defined primarily by the light-absorbing component (up to 97% of the cost) while the material selection for the electrolysis components has, to a large extent, minor effects. The findings presented here can help direct research and development efforts towards the fabrication of deployable solar-hydrogen generators that are cost competitive with commercial energy sources.