The H + CH(+) reaction is studied by quasiclassical trajectory (QCT) calculations, along with phase space theory (PST) and quantum rigid rotor calculations, employing a global single-valued potential energy surface recently derived by our group. We report QCT total cross sections for each of the three channels, for low collision energies and different reactant rotational quantum numbers. At the lowest collision energies, all cross sections exhibit a capture-like behaviour, as expected from a barrierless reaction. At higher energies, there are important dynamical effects coming from the opening of new channels in the inelastic and reactive exchange collisions. The inelastic cross sections turn out to largely increase, while the reactive abstraction cross sections are declining faster than predicted by the capture theory. A large value of the reactant rotational quantum number tends to suppress these dynamical effects. The QCT rate coefficients are reported for a temperature range from 1-700 K. Below 20 K, the abstraction and exchange QCT rate coefficients are almost constant, as predicted by the capture theory. Above this temperature, the abstraction rate coefficient declines, while the exchange and inelastic rate coefficients are increasing, due to the opening of new channels. A good agreement is observed between the experimental abstraction rate coefficient and the QCT and PST ones. The QCT inelastic results are also compared with those obtained from rigid rotor close coupling (CCRR) calculations in order to check the ability of this approach to provide a reliable estimate of the inelastic rate coefficients for a reactive system without a barrier. The laws of variation as a function of temperature are found to be very similar and the curves are parallel above 20 K. However, reaction is not allowed in the rigid rotor approximation, therefore the CCRR results are about twice as large as their QCT counterparts.