For low-resolution analog-to-digital converter (ADC) systems, only high-complexity receive antenna selection has been developed and transmit antenna selection has been limited to a single antenna selection in prior work. In this paper, we propose low-complexity receive antenna selection algorithms and analyze transmit antenna selection by considering antenna selection at a base station with large antenna arrays and low-resolution ADCs. For downlink antenna selection, we show a selection criterion with zero-forcing precoding equivalent to a perfect quantization system; sum rate increases with number of selected antennas; derivation of the sum rate loss function from using a antenna subset; and sum rate loss reaches a maximum at a point of total transmit power and decreases beyond that point to converge to zero. For wideband orthogonal-frequency-division-multiplexing (OFDM) systems, our results hold when entire subcarriers share a common subset of antennas. For uplink antenna selection, we generalize a greedy antenna selection criterion; propose a quantization-aware fast antenna selection algorithm using the criterion; and derive a lower bound on sum rate achieved by the proposed algorithm. For wideband OFDM systems, we extend our algorithm and derive a lower bound on its sum rate. Simulation results validate theoretical analyses and show increases in sum rate over conventional algorithms.