The sensor selection problem arises when multiple sensors are jointly trying to estimate a process but only a subset of them can take and/or use measurements at any time step. In a networked estimation situation, sensors are typically equipped with some memory and processing capabilities. We illustrate that utilization of these capabilities can lead to significant performance gains in the sensor selection problem for improved inference. Further, it also leads to significant pruning of the search tree that yields the optimum sensor schedule. We also present a periodicity result for the case where the decision is whether the sensor should transmit or not.