Using all-atom molecular simulation, a wide range of plasticizers for poly(vinyl chlorid) (PVC), including ortho- and tere-phthalates, trimellitates, citrates, and various aliphatic dicarboxylates, are systematically studied. We focus on the effects of plasticizer molecular structure on its performance, as measured by performance metrics including its thermodynamic compatibility with PVC, effectiveness of reducing the material's Young's modulus, and migration rate in the PVC matrix. The wide variety of plasticizer types covered in the study allows us to investigate the effects of seven molecular design parameters. Experimental findings about the effects of plasticizer molecular design are also compiled from various literature sources and reviewed. Comparison with experiments establishes the reliability of our simulation predictions. The study aims to provide a comprehensive set of guidelines for the selection and design of high-performance plasticizers at the molecular level. Molecular mechanisms for how each design parameter influences plasticizer performance metrics are also discussed. Moreover, we report a nontrivial dependence of plasticizer migration rate on temperature, which reconciles seemingly conflicting experimental reports on the migration tendency of different plasticizers.