Large linear positive magnetoresistance (LPMR) in topological and magnetic materials remains a subject of intense debate, particularly in noncollinear spin systems where spin-dependent scattering complicates charge transport. Manganese phosphide (MnP), a helimagnetic binary pnictide with multiple field-induced magnetic transitions, provides a useful platform to investigate the interplay between complex magnetism and electronic topology. Here, we present a comprehensive experimental and theoretical investigation of phase-dependent magnetotransport in high-quality MnP single crystals. Hall measurements reveal an anomalous Hall effect dominated by skew scattering at high temperatures and a finite topological Hall effect in the noncollinear fan (FAN) and low-temperature screw (SCR) phases. At low temperatures, we observe a large, non-saturating LPMR reaching nearly 800 percent at 4 K and 15 T, with a pronounced linear field dependence in the field-polarized ferromagnetic (FM2) state. First-principles calculations reveal a strongly anisotropic semi-Dirac-like band at the Y point that progressively approaches the Fermi level from the SCR to FAN and FM2 states. Our analysis indicates that the resulting small Fermi pocket can access the extreme quantum-limit regime at experimentally accessible fields, providing a microscopic framework for the observed LPMR within Abrikosov's quantum magnetoresistance theory.