Density-functional theory calculations are performed to examine how two characteristics of a trivalent dopant (the one, physical - the ionic radius, the other, chemical - the electronegativity) impact the thermodynamics of doping, the defect association energy and the hydration energy in barium stannate, a perovskite oxide candidate as an electrolyte for Solid Oxide or Protonic Ceramic Fuel Cells. The formation energies of several trivalent dopants currently used in experimental works are computed in different external conditions and on the two possible sites (Ba, Sn), in their ionized state. These dopants cover a wide range of ionic radii (from 0.62 to 1.03 angstrom) and can be divided in two families according to their electronegativity: elements of group IIIA (Ga, In), versus IIIB transitions metals and Rare Earths (Sc, Lu, Y, Gd, Sm, La). The oxygen vacancy and the protonic defect are also studied, either isolated or in the vicinity of the dopant substituted on Sn site (1st & 2nd neighbors). The association energy between the dopant and both the oxygen vacancy and the proton, as well as the formation energy of the dopant on the Ba site, are mainly governed by the ionic radius of the dopant, with the exception that electronegative dopants stabilize more the oxygen vacancy in their vicinity. Therefore, a subtle interplay between elastic effects and chemistry is found to control the hydration energy/enthalpy, the more electronegative dopants indium particularly producing, at given radius, a less stable hydrated state. We provide with general trends likely to help experimentalists in the design of new materials, regarding the choice of dopant.