What is an optimal particle shape for scattering, e.g., shape causing minimal extinction among those of equal volume and randomly oriented? Guided by the isoperimetric property of a sphere, relevant in the geometrical optics limit of scattering by large particles, we examine an analogous question in the low frequency (induced dipole moment) approximation, seeking to disentangle electric and geometric contributions. To that end, a simple proof is supplied of spherical optimality for a coated ellipsoidal particle and a monotonic increase with asphericity is shown in the low frequency regime for orientation-averaged induced dipole moments and scattering cross-sections. Physical insight is obtained from the Rayleigh-Gans (transparent) limit and eccentricity expansions. We propose linking small and large particle regime in a single minimum principle valid for all size parameters, provided that reasonable size distributions wash out the Mie resonances. This proposal is further supported by the sum rule for integrated extinction. Implications for atmospheric remote sensing are discussed.