The development of Internet of Things (IoT) networks causes an increasing demand for high-quality video streaming, which results in the burden of traditional mobile cloud computing (MCC) networks, such as high energy consumption and dissatisfaction with the user's Quality of Experience (QoE). To address this issue, mobile-edge computing (MEC) networks have recently been widely employed for high-quality video streaming scenarios under time-varying wireless channels. However, in MEC networks, limited resources deteriorate the video transmission rate and the quality of videos. Therefore, in this article, we investigate a MEC network with cloud-edge integration for adaptive bitrate (ABR) video streaming, where the edge server (ES) performs cloud-edge selection to decide whether the requested video should be directly obtained from the cloud server (CS) or through a transcoding process. We first design edge caching and transcoding processes to enhance resource utilization and reduce computational consumption through bitrate adaptation strategy and cloud-edge selection decision. Moreover, we utilize the energy efficiency by jointly considering the user's QoE and energy consumption to measure the network's performance, and then formulate the optimization objective to maximize energy efficiency. In further, we employ a deep deterministic policy gradient (DDPG)-based scheme to solve the optimization problem by applying video quality adaptation technique, allocating computational resources and transmit power. Finally, simulation results demonstrate that the proposed scheme accomplishes superior energy efficiency compared to the competing schemes at least 41.1%.