Beamspace millimeter-wave (mmWave) and terahertz (THz) massive MIMO constitute attractive schemes for next-generation communications, given their abundant bandwidth and high throughput. However, their user and beam selection problem has to be efficiently addressed. Inspired by this challenge, we develop low-complexity solutions explicitly. We introduce the dirty paper coding (DPC) into the joint user and beam selection problem. We unveil the compelling properties of the DPC sum rate in beamspace massive MIMO, showing its monotonic evolution against the number of users and beams selected. We then exploit its beneficial properties for substantially simplifying the joint user and beam selection problem. Furthermore, we develop a set of algorithms striking unique trade-offs for solving the simplified problem, facilitating simultaneous user and beam selection based on partial beamspace channels for the first time. Additionally, we derive the sum rate bound of the algorithms and analyze their complexity. Our simulation results validate the effectiveness of the proposed design and analysis, confirming their superiority over prior solutions.