A strong inhomogeneous static electric field is used to spatially disperse a supersonic beam of polar molecules, according to their quantum state. We show that the molecules residing in the lowest-lying rotational states can be selected and used as targets for further experiments. As an illustration, we demonstrate an unprecedented degree of laser-induced one-dimensional alignment (cos;(2)theta_(2D)=0.97) and strong orientation of state-selected iodobenzene molecules. This method should enable experiments on pure samples of polar molecules in their rotational ground state, offering new opportunities in molecular science.