A comprehensive study of the static and dynamic critical properties of the quasi-two-dimensional antiferromagnet MnPS3 is presented. The relatively large spin S=5/2 of the Mn ions ensure predominantly classical behavior, and the compound is believed to be a good example of a Heisenberg-type system on a honeycomb lattice. The sample has been measured using a variety of neutron-scattering techniques and instrumentation. The results are compared to the three-dimensional (3D) Heisenberg model, the two-dimensional classical O(3) rotator model, the two-dimensional XY model, and the related two-dimensional anisotropic Heisenberg model. The critical properties appear to be best described by the last model almost entirely over the measured temperature range, except just below the Neel temperature where the critical behavior seems to be 3D. There are some discrepancies, particularly in the rescaling of the spin stiffness and the energy widths of the structure factor. A possible explanation for the XY-like behavior is offered, involving the magnetic anisotropy in the system and its influence on the Hamiltonian.