This work studies a variant of hybrid beamforming, namely, hybrid beamforming with selection (HBwS), as an attractive solution to reduce the hardware cost of multi-user Massive Multiple-Input-Multiple-Output systems, while retaining good performance. Unlike conventional hybrid beamforming, in a transceiver with HBwS, the antenna array is fed by an analog beamforming matrix with $\bar{L}$ input ports, where $\bar{L}$ is larger than the number of up/down-conversion chains $\bar{K}$. A bank of switches connects the instantaneously best $\bar{K}$ out of the $\bar{L}$ input ports to the up/down-conversion chains. The analog beamformer is designed based on average channel statistics and therefore needs to be updated only infrequently, while the switches operate based on instantaneous channel knowledge. HBwS allows use of simpler hardware in the beamformer that only need to adjust to the statistics, while also enabling the effective analog beams to adapt to the instantaneous channel variations via switching. This provides better user separability, beamforming gain, and/or simpler hardware than some conventional hybrid schemes. In this work, a novel design for the analog beamformer is derived and approaches to reduce the hardware and computational cost of a multi-user HBwS system are explored. In addition, we study how $\bar{L}$, the switch bank architecture, the number of users and the channel estimation overhead impact system performance.