One of the fundamental aspects of cellular material design is cell shape selection. Of particular interest is how this selection can be made in the context of a realistic three-dimensional structure. Towards this goal, this work studied the stiffness response of periodic and stochastic lattice structures for the loading conditions of bending, torsion and tension/compression using commercially available lattice design optimization software. The goal of this computational study was to examine the feasibility of developing a ranking order based on minimum compliance or maximum stiffness for enabling cell selection. A study of stochastic shapes with different seeds was also performed. Experimental compression testing was also performed to validate a sample space of the simulations. The findings of this study suggest that under certain circumstances, stochastic shapes have the potential to generate the highest stiffness-to-weight ratio in the test environments considered.