Exclusive photoproduction of mesons is studied using the H1 detector at the collider HERA. A sample of about 900000 events is used to measure single- and double-differential cross sections for the reaction . Reactions where the proton stays intact () are statistically separated from those where the proton dissociates to a low-mass hadronic system ( GeV). The double-differential cross sections are measured as a function of the invariant mass of the decay pions and the squared 4-momentum transfer at the proton vertex. The measurements are presented in various bins of the photon-proton collision energy . The phase space restrictions are GeV, GeV, and GeV. Cross section measurements are presented for both elastic and proton-dissociative scattering. The observed cross section dependencies are described by analytic functions. Parametrising the dependence with resonant and non-resonant contributions added at the amplitude level leads to a measurement of the meson mass and width at (tot.) MeV and (tot.) MeV, respectively. The model is used to extract the contribution to the cross sections and measure it as a function of and . In a Regge asymptotic limit in which one Regge trajectory dominates, the intercept (tot.) and the slope (tot.) GeV of the dependence are extracted for the case .