This paper presents a class of 3D single-scale isotropic materials with tunable stiffness and buckling strength obtained via topology optimization and subsequent shape optimization. Compared to stiffness-optimal closed-cell plate material, the material class reduces the Young's modulus to a range from 79% to 58%, but improves the uniaxial buckling strength to a range from 180% to 767%. Based on small deformation theory, material stiffness is evaluated using the homogenization method. Buckling strength under a given macroscopic stress state is estimated using linear buckling analysis with Block-Floquet boundary conditions to capture both short and long wavelength buckling modes. The 3D isotropic single-scale materials with tunable properties are designed using topology optimization, and are then further simplified using shape optimization. Both topology and shape optimized results demonstrate that material buckling strength can be significantly enhanced by hybrids between truss and variable thickness plate structures.