Proximity networking attracts increasing interests in recent years, where UE-to-Network relaying becomes an effective functionality to connect more User Equipments (UEs) to the network. In this functionality, Relay UE provides functionality to support connectivity to the network for Remote UE(s) in proximity. Remote UEs establish communication links with Relay UEs through direct discovery and relay selection, where the quality of discovering and selecting algorithms will be the key to affecting the final connection performance. In this paper, we investigate the discovery and selection of the UE-to-Network relay by considering multidimensional indexes, and we propose a new Adaptive Relay UE Selection (ARUES) Strategy for Remote UE to discovery and choose a suitable Relay UE in two scenarios. We evaluate our proposed strategy with several performance metrics, and compare them with those of Random Selecting (RS) and Greatest Relay Signal Strength (GRSS). Simulation results show that our proposed strategy performs the best, compared with other strategies.