We report a detailed Density Functional Theory (DFT) based investigation of the structure and stability of bulk and surface structures for the Group 10-12 elements Pd, Cu and Zn, considering the effect of the choice of exchange-correlation density functionals and computation parameters. For the initial bulk structures, the lattice parameter and cohesive energy are calculated, which are then augmented by calculation of surface energies and work functions for the lower-index surfaces. Of the 22 density functionals considered, we highlight the mBEEF density functional as providing the best overall agreement with experimental data. The optimal density functional choice is applied to the study of higher index surfaces for the three metals, and Wulff constructions performed for nanoparticles with a radius of 11nm, commensurate with nanoparticle sizes commonly employed in catalytic chemistry. For Pd and Cu, the low-index (111) facet is dominant in the constructed nanoparticles, covering ~50% of the surface, with (100) facets covering a further 10 to 25%; however, non-negligible coverage from higher index (332), (332) and (210) facets are also observed for Pd, and (322), (221) and (210) surfaces are observed for Cu. In contrast, only the (0001) and (10-10) facets are observed for Zn. Overall, our results highlight the need for carefully validation of computational settings before performing extensive density functional theory investigations of surface properties and nanoparticle structures of metals.