This paper considers a millimeter-wave wideband point-to-point MIMO system with fully digital transceivers at the base station and the user equipment (UE), focusing on mobile UE scenarios. A main challenge when building a digital UE combining is the large volume of baseband samples to handle. To mitigate computational and hardware complexity, we propose a novel two-stage digital combining scheme at the UE. The first stage reduces the N_r received signals to N_c streams before baseband processing, leveraging channel geometry for dimension reduction and updating at the beam coherence time, which is longer than the channel coherence time of the small-scale fading. By contrast, the second-stage combining is updated per fading realization. We develop a pilot-based channel estimation framework for this hardware setup based on maximum likelihood estimation in both uplink and downlink. Digital precoding and combining designs are proposed, and a spectral efficiency expression that incorporates imperfect channel knowledge is derived. The numerical results demonstrate that the proposed approach outperforms hybrid beamforming, showcasing the attractiveness of using two-stage fully digital transceivers in future systems.