The development of cellular solids is one of the research fields in which additive manufacturing has made relevant progress in producing lightweight components and enhancing their performance. This work presents comprehensive research on the mechanical performance of fused filament fabricated three-dimensional lightweight cellular solids, including open-cell and closed-cell lattice designs and triply periodic minimal surfaces (TPMS), with different cell sizes and infill densities. The aim of this work is to determine the range and limits of the achievable mechanical behavior by employing different cell designs made from a single material and manufacturing technique. Experimental results obtained with cell designs fabricated with a high-performance polymer (PEI Ultem) showed wide ranges of effective stiffnesses from 1 to 293 MPa, strengths from 0.1 to 18.1 MPa, and densities from 0.066 to 0.541 g/cm3. Furthermore, two validated numerical approaches are provided to simulate their mechanical performance accurately. Moreover, a novel and robust index to quantify the isotropy of additively manufactured cellular solids based on the graphical representation of the homogenized stiffness tensor is proposed. Finally, experimental evidence states that the Shell-TPMS designs proved to be the most efficient cellular pattern, followed by the Skeletal-TPMS and the lattice configurations.