Continuous demand for improvement of material performance in structural applications pushes the need for materials that are able to fulfill multiple functions. Extensive work on effective static properties of different architected materials have shown their ability to push the modulus-density design space, in terms of high effective moduli at low relative density. On the other hand, variations in geometry allow for these materials to manipulate mechanical wave propagation, producing band gaps at certain frequency ranges. The enhanced static and vibration properties of architected metamaterials make them ideal candidates for multi-functional purposes. In this paper, we take inspiration from the mass-efficient static behavior of different lattice geometries to fully explore the capabilities of a periodic and locally resonant metastructure design platform. We numerically study the influence of four different lattice topologies on the dynamic and static behavior of metastructures that combine a periodic lattice geometry with locally resonant inclusions. We analyze the influence of lattice geometry on band gap frequencies in terms of the lattice effective static properties. We show that vibration mitigation over a wide range of frequencies is achieved by tailoring the lattice geometry for constant unit cell mass and size. Specifically, by selectively placing material inside the unit cell, we achieve up to a 6-fold change of lower edge band gap frequency and up to an 8-fold change of normalized band gap width, for metastructures with low-density lattices. We introduce multi-functional performance parameters to evaluate the metastructures in terms of their effective static stiffness and band gap properties. These parameters can inform the design of tailored materials that have desired mechanical and dynamic properties for applications in e.g., aerospace and automotive components, and energy infrastructure.