A theoretical treatment is developed for the wetting of a solid particle at an oil-water interface in terms of the components of the surface energies of all three phases. Calculated oil-water contact angles for a solid of given hydrophobicity with a range of oils of different polarity show good agreement with experimental data. For a hydrophobically modified silica surface, oils of increasing polarity give higher oil-water contact angles measured through water. The results are in line with the effect of oil type on Pickering emulsion type where more polar oils preferentially give water-in-oil emulsions. The approach is also used to predict the type of solid particles that would be required to stabilize emulsions of two immiscible oils. For hydrocarbon-fluorocarbon pairs, it is predicted that perfluorinated particles would stabilize fluorocarbon-external emulsions while silica particles with a high coverage of hydrocarbon groups should stabilize hydrocarbon-external emulsions.