In distributed source localization where sensors transmit measurements to a fusion node, we address the sensor selection problem where the goal is to find the best set of sensors that maximizes localization accuracy when quantization of sensor measurements is taken into account. Since sensor selection depends heavily upon rate assigned to each sensor, joint optimization of rate allocation and sensor selection is required to achieve the best solution. We show that this task could be accomplished by solving the problem of allocating rates to each sensor so as to minimize the error in estimating the position of a source. Then we solve this rate allocation problem by using the generalized BFOS algorithm. Our experiments demonstrate that the best set of sensors obtained from the proposed sensor selection algorithm leads to significant improvements in localization performance with respect to the set of sensors determined from a sensor selection process based on unquantized measurements.