We propose control and communication strategies for nonlinear networked control systems subject to state and input constraints. The objective is to steer the state of the system toward a prescribed target set in finite time (reachability), while at the same time remaining inside a safety set for all time (safety). By leveraging the notion of the $\delta$-input-to-state stability (ISS) control Lyapunov function, we derive a sufficient condition to generate a communication scheduling, such that the resulting state trajectory guarantees reachability and safety. Moreover, in order to alleviate computational burden, we present a way to find a suitable communication scheduling by implementing abstraction schemes and standard graph search methodologies. Simulation examples validate the effectiveness of the proposed approach.