Optimal sensor selection for source parameter estimation in energy harvesting Internet of Things (IoT) networks is studied in this paper. Specifically, the focus is on the selection of the sensor locations which minimizes the estimation error at a fusion center, and to optimally allocate power and bandwidth for each selected sensor subject to a prescribed spectral and energy budget. To do so, measurement accuracy, communication link quality, and the amount of energy harvested are all taken into account. The sensor selection is studied under both analog and digital transmission schemes from the selected sensors to the fusion center. In the digital transmission case, an information theoretic approach is used to model the transmission rate, observation quantization, and encoding. We numerically prove that with a sufficient system bandwidth, the digital system outperforms the analog system with a possibly different sensor selection. The design problem of interest is a Boolean non convex optimization problem, which is solved by relaxing the Boolean constraints. To efficiently round the obtained relaxed solution, we propose a randomized rounding algorithm which generalizes the existing algorithm.