Plasma-facing materials (PFMs) represent one of the most significant challenges for the design of future nuclear fusion reactors. Inside the reactor, the divertor will experience the harshest material environment: intense bombardment of neutrons and plasma particles coupled with extremely large and intermittent heat fluxes. The material designated to cover this role in ITER is tungsten. While no other materials have shown the potential to match the properties of tungsten, many drawbacks associated with its application remain, including cracking and erosion induced by a low recrystallization temperature combined with a high ductile-brittle transition temperature and neutron-initiated embrittlement; surface morphology changes (helium bubbles and fuzz layer) due to plasma-tungsten interaction with subsequent risk of spontaneous material melting and delamination; and low oxidation resistance in the case of air contamination. Exploring alternatives to tungsten requires the design of a multivariable optimization problem. This work aims to produce a structured and comprehensive material screening of PFM candidates based on known inorganic materials. The method applied in this study to identify the most promising PFM candidates combines peer-reviewed data present in the PAULING FILE database and first-principles density-function theory calculations focusing on two key PFM defects - namely, the sputtering of surface atoms and the incorporation of interstitial hydrogen, respectively characterized by the surface binding energy and the interstitial formation energy. The crystal structures and their related properties, extracted from the PAULING FILE, are ranked according to the heat-balance equation of a PFM subjected to the heat loads in the divertor region of an ITER-like tokamak. The materials satisfying the requirements are critically compared with the state-of-the-art in plasma-facing materials research and in studies of refractory materials exposed to high temperatures, plasma, and neutron bombardment. This comparison assesses their thermo-mechanical properties under such conditions, identifying a subset of promising materials for first-principles electronic structure calculations. Most previously known and extensively studied PFMs, such as tungsten, molybdenum, and carbon-based materials, are captured by this screening process, confirming its reliability. Additionally, less familiar refractory materials suggest performance that calls for further investigations.