A crucial step in the preparation of supported metal catalysts is related to the choice of support, since it regulates the anchoring of the metal species in an environment of strong interactions. In this sense, the binding on the support, which may present defects, as well as induced modifications of the electronic structure, helps to determine efficient metal/support combinations for catalysis applications. In this work, first-principles studies have been carried out to model and describe the geometric and electronic properties of O-functionalized graphene as a model carbon support, in addition to a single Pd atom and Pd13 nanocluster (experimentally observed on various carbon supports) as supported metal catalysts. The carbon-based nanomaterial includes experimentally probed abundant oxygen functional groups and point defects, demonstrating high thermal stability at room temperature. The characterization confirms the structural motifs presented in the model, distinguishing the organic functionalities and various defects using spectroscopy techniques. Interestingly, the oxygenated carbon-based support presents a metallic character when the formal charges in the embedded Pd atom and nanocluster have been determined to be [Pd]+ and [Pd13]3+. The hydrogenation process of the adsorbed cluster is also presented, with the determination of a ratio between the adsorbed hydrides and the surface metal atoms close to unity at room temperature, thanks to ab initio molecular dynamics.