Collisional ring galaxies are the outcome of nearly axisymmetric high-speed encounters between a disc and an intruder galaxy. We investigate the properties of collisional ring galaxies as a function of the impact parameter, the initial relative velocity and the inclination angle. We employ new adaptive mesh refinement simulations to trace the evolution with time of both stars and gas, taking into account star formation and supernova feedback. Axisymmetric encounters produce circular primary rings followed by smaller secondary rings, while off-centre interactions produce asymmetric rings with displaced nuclei. We propose an analytical treatment of the disc warping induced by an inclination angle greater than zero. The star formation history of our models is mainly influenced by the impact parameter: axisymmetric collisions induce impulsive short-lived starburst episodes, whereas off-centre encounters produce long-lived star formation. We compute synthetic colour maps of our models and we find that rings have a B - V colour typically ∼0.2 mag bluer than the inner and outer disc, in agreement with observations.