Unmanned aerial vehicle (UAV)-enabled communications have been proposed as a critical part of the beyond fifth-generation (5G) cellular networks. This type of communications is frequently characterized by line-of-sight (LoS) and dynamic propagation conditions. However, in various scenarios, the presence of large obstacles in the LoS path is unavoidable, resulting in shadowed fading environments. In this paper, a new channel model is proposed, in which the effects of mobility and shadowing are simultaneously considered. In particular, the performance of a UAV-based communication system operating in a shadowed double-scattering channel is analyzed. {The new channel model is generic, since it models various fading/shadowing conditions, while it is in terms of easy-to-evaluate mathematical functions. Moreover, a low complexity UAV selection policy is proposed, which exploits shadowing-related information. The proposed scheme offers a reduction of the signal processing complexity, without any important degradation on the performance, as compared to alternatives approaches.} In this context, a new analytical framework has been developed for investigating the performance of the new strategy. Finally, the main outcomes of this paper are also validated by empirical data, collected in an air-to-ground measurement campaign.