Using a numerically accurate radiation-gasdynamical method we investigate the interacting winds scenario for spherically symmetric Planetary Nebulae (PNe). Our models include the interaction of three.winds: a fast, low mass-loss rate wind; a slow high mass-loss rate wind (a ''superwind''); and a slow, moderate mass-loss rate wind (an AGB wind). Our model also includes the evolution of the UV spectrum of the PNe central star. The radiation from the central star is transferred through the interacting winds, altering the microphysical conditions. Using a time-dependent treatment of ionization processes we calculate, self-consistently, the emissivities of a number of observationally important recombination, permitted and forbidden lines. In this way we are able to produce ''synthetic observations'' of model morphology, kinematics, and ionization structure. We find that the models evolve through four distinct phases with distinct observational characteristics. The character of each of the four phases is determined by the evolution and interaction of gasdynamic and radiation discontinuities (shocks, rarefactions, ionization fronts) which are driven through the winds. We find the radiation and gasdynamics to be well coupled. The evolution of these shock waves and ionization fronts is largely determined by the initial conditions in the models. We find good qualitative agreement between the observational properties of the models and the characteristic morphology, kinematics, and ionization structures observed in real PNe. In particular we find that the four evolutionary phases seen in the simulations allow these models to embrace the diversity of PNe observations and, furthermore, allow spherical PNe to be drawn under the umbrella of a single evolutionary scenario. On the other hand the differences in the appearance of the models in the four phases argues that care must be taken when interpreting observations. These models show that the dynamical evolution of PNe will be complex but regular. Some effort at understanding which evolutionary phase an individual PN is in should be made before properties of the nebula are derived from observations.