The rapid growth of the so-called Internet of Things is expected to significantly expand and support the deployment of resource-limited devices. Therefore, intelligent scheduling protocols and technologies such as wireless power transfer, are important for the efficient implementation of these massive low-powered networks. This paper studies the performance of a wireless powered communication network, where multiple batteryless devices harvest radio-frequency from a dedicated transmitter in order to communicate with a common information receiver (IR). We investigate several novel selection schemes, corresponding to different channel state information requirements and implementation complexities. In particular, each scheme schedules the $k$-th best device based on: a) the end-to-end (e2e) signal-to-noise ratio (SNR), b) the energy harvested at the devices, c) the uplink transmission to the IR, and d) the conventional/legacy max-min selection policy. We consider a non-linear energy harvesting (EH) model and derive analytical expressions for the outage probability of each selection scheme by using tools from high order statistics. %Our results show that, the performance of all the proposed schemes converges to an error floor due to the saturation effects of the considered EH model. Moreover, an asymptotic scenario in terms of the number of devices is considered and, by applying extreme value theory, the system's performance is evaluated. We derive a complete analytical framework that provides useful insights for the design and realization of such networks.