This paper addresses the beam-selection challenges in Multi-User Multiple Input Multiple Output (MU-MIMO) beamforming for mm-wave and THz channels, focusing on the pivotal aspect of spectral efficiency (SE) and computational efficiency. We introduce a novel approach, the Greedy Interference-Optimized Singular Vector Beam-selection (G-IOSVB) algorithm, which offers a strategic balance between high SE and low computational complexity. Our study embarks on a comparative analysis of G-IOSVB against the traditional IOSVB and the exhaustive Singular-Vector Beamspace Search (SVBS) algorithms. The findings reveal that while SVBS achieves the highest SE, it incurs significant computational costs, approximately 162 seconds per channel realization. In contrast, G-IOSVB aligns closely with IOSVB in SE performance yet is markedly more computationally efficient. Heatmaps vividly demonstrate this efficiency, highlighting G-IOSVB's reduced computation time without sacrificing SE. We also delve into the mathematical intricacies of G-IOSVB, demonstrating its theoretical and practical superiority through rigorous expressions and detailed algorithmic analysis. The numerical results illustrate that G-IOSVB stands out as an efficient, practical solution for MU-MIMO systems, making it a promising candidate for high-speed, high-efficiency wireless communication networks.