Rydberg positronium (Ps) atoms have been prepared in selected Stark states via two-step (1s→2p→nd/ns) optical excitation. Two methods have been used to achieve Stark-state selection: a field ionization filter that transmits the outermost states with positive Stark shifts, and state-selected photoexcitation in a strong electric field. The former is demonstrated for n=17 and 18 while the latter is performed for n=11 in a homogeneous electric field of 1.9  kV/cm. The observed spectral intensities and their dependence on the polarization of the laser radiation are in agreement with calculations that include the perturbations of the intermediate n=2 manifold. Our results pave the way for the generation of Rydberg Ps atoms with large electric dipole moments that are required for the realization of schemes to control their motion using inhomogeneous electric fields, an essential feature of some proposed Ps free-fall measurements requiring focused beams of long-lived atoms.