The Fourier grid method has been implemented on four tri-atomic coordinate systems. The explicit forms of the kinetic-energy operators are presented and the method of implementation described. The coordinates tested are the perimetric, Eckart, Jacobi, and conformal Euclidean. A comparative study was carried out using propagation techniques to obtain the lowest vibrational eigenvalues on the H-3(+) and the van der Waals Na...FH molecules for J=0. Converged eigenvalues were obtained for all the coordinate systems tested. The wavepacket representation methods were also compared for the nonadiabatic photodissociation dynamics of the Na...FH. When the coordinate systems matched the topology of the potential-energy surface, significant reduction in the grid size was obtained. The analysis has led to a method for evaluating grid efficiency and optimization based on a classical phase space approach.