This work systematically investigates the microstructure-property relationship in Mg alloys. Emphasis is placed on understanding, through high resolution crystal plasticity modeling, how grain size and texture collectively impact material strengthening and hardening, net plastic anisotropy, and tension-compression asymmetry. To achieve this, 528 fully three-dimensional finite element calculations are performed, which comprise eleven textures, four grain sizes, six loading orientations, and two uniaxial loading states (tension and compression). The grain size effect follows Hall-Petch relation that depends on both, loading orientation and initial texture. The reduction in extension twinning with grain size refinement is influenced by texture as well. Below a threshold textural strength, grain size refinement leads to an appreciable reduction in the net plastic anisotropy at yield, quantified using Hill anisotropy, and reduced tension-compression asymmetry. Using a micromechanical basis, the effect of grain size and texture on material ductility is predicted to be non-monotonic. The computational predictions serve as synthetic data sets for experimental validation and reduced-order modeling.