Precoding/combining and large antenna arrays are essential in millimeter wave (mmWave) systems. In traditional MIMO systems, precoding/combining is usually done digitally at baseband with one radio frequency (RF) chain and one analog-to-digital converter (ADC) per antenna. The high cost and power consumption of RF chains and ADCs at mmWave frequencies make an all-digital processing approach prohibitive. When only a limited number of RF chains is available, hybrid architectures that split the precoding/combining processing into the analog and digital domains are attractive. A previously proposed hybrid solution employs phase shifters and mixers in the RF precoding/combining stage. It obtains near optimal spectral efficiencies with a reduced number of RF channels. In this paper we propose a different hybrid architecture, which simplifies the hardware at the receiver by replacing the phase shifters with switches. We present a new approach for compressed sensing based channel estimation for the hybrid architectures. Given the channel estimate, we propose a novel algorithm that jointly designs the antenna subsets selected and the baseband combining. Using power consumption calculations and achievable rates, we compare the performance of hybrid combining with antenna switching and phase shifting, showing that antenna selection is preferred in a range of operating conditions.