This paper presents an estimation approach within the framework of uplink massive machine-type communications (mMTC) that considers the energy limitations of the devices. We focus on a scenario where a group of sensors observe a set of parameters and send the measured information to a collector node (CN). The CN is responsible for estimating the original observations, which are spatially correlated and corrupted by measurement and quantization noise. Given the use of Gaussian sources, the minimum mean squared error (MSE) estimation is employed and, when considering temporal evolution, the use of Kalman filters is studied. Based on that, we propose a device selection strategy to reduce the number of active sensors and a quantization scheme with adjustable number of bits to minimize the overall payload. The set of selected sensors and quantization levels are, thus, designed to minimize the MSE. For a more realistic analysis, communication errors are also included by averaging the MSE over the error decoding probabilities. We evaluate the performance of our strategy in a practical mMTC system with synthetic and real databases. Simulation results show that the optimization of the payload and the set of active devices can reduce the power consumption without compromising the estimation accuracy.