Here we present a Density Functional Theory (DFT) study on the suitability of modern corrections for the inclusion of dispersion related terms (DFT-D) in treating the interaction of graphene and metal surfaces, exemplified by the graphene/Ni(111) system. The Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional is used as basis, on top of which we tested the family of Grimme corrections (D2 and D3, including Becke-Jonson damping and Andersson approach) as well as different flavors of the approach by Tkatchenko and Scheffler (TS). Two experimentally observed chemisorbed states, top-fcc and bridge-top conformations, were examined, as well as one physisorbed situation, the hcp-fcc state. Geometric, energetic, and electronic properties were compared to sets of experimental data for our model system of graphene/Ni(111), but also for available data of bulk Ni, graphite, and free-standing graphene. Results show that two of the most recent approximations, the fully ab initio TS-MBD, and the semi-empirical Grimme D3 correction are best suited to describe graphene↔metal contacts, yet, comparing to earlier studies, the Rev-vdW-DF2 functional is also a good option, whereas optB86-vdW and optB88b-vdW functionals are fairly close to experimental values to be harmless used. The present results highlight how different approaches for the approximate treatment of dispersive forces yield different results, and so finetuning and testing of the envisioned approach for every specific system is advisable. The present survey clears the path for future accurate and affordable theoretical studies of nanotechnologic devices based on graphene-metal contacts.