Outflows from starburst galaxies can be driven by thermal pressure, radiation, and cosmic rays. We present an analytic phenomenological model that accounts for these contributions simultaneously to investigate their effects on the hydrodynamical properties of outflows. We assess the impact of energy injection, wind opacity, magnetic field strength, and the mass of the host galaxy on flow velocity, temperature, density, and pressure profiles. For an M82-like wind, a thermally dominated driving mechanism is found to deliver the fastest and hottest wind. Radiation-driven winds in typical starburst-galaxy configurations are unable to attain the higher flow velocities and temperatures associated with thermal and cosmic ray-driven systems, leading to higher wind densities which would be more susceptible to cooling and fragmentation at lower altitudes. High opacity winds are more sensitive to radiative driving, but terminal flow velocities are still lower than those achieved by other driving mechanisms at realistic opacities. We demonstrate that variations in the outflow magnetic field can influence its coupling with cosmic rays, where stronger fields enable greater streaming but less driving near the base of the flow, instead with cosmic rays redirecting their driving impact to higher altitudes. The gravitational potential is less important in M82-like wind configurations, and substantial variations in the flow profiles only emerge at high altitude in massive haloes. This model offers a more generalized approach to examine the large-scale hydrodynamical properties for a wide variety of starburst galaxies.