In this two-part article, we propose a framework for selecting ferroelectric oxide material for the design of a negative capacitance field-effect transistor (NCFET). The investigation is based on an exhaustive search of two important ferroelectric material parameters: remnant polarization and coercive field in the context of their negative capacitance properties. The effects of these parameters are first studied at the NCFET device level and systematically extended up to the full-chip level. Based on this search, we arrive at the notion of optimality of ferroelectric parameters for a given 'isoperformance full-chip benchmark': The power dissipation in a specific circuit/system is maximally reduced by using optimized NCFETs while meeting the target performance. In Part I, we develop the framework for identifying optimal ferroelectric parameters at a given VDD. This sets the stage for Part II, where we investigate the optimal ferroelectric parameters as VDD is scaled.