If meant for an industrially-sized plant: cheap, available on short notice, easily recoverable for recycling (e.g., a lower BP than extract and raffinate), chemically and thermally stable, non toxic, non corrosive, selective at ambient temperatures for the specific extraction purpose, soluble (to reduce needed dosage), easily separable at the extraction step by density differences, bio-degradable, low latent heat of vaporization, available commercial knowhow, sometimes it is desirable that the solvent has a low boiling heterogeneous azeotrope with water. Did I forget to mention any other desirable characteristic ?