A systematic study on the parameter space of graphene CVD on polycrystalline Cu foils is presented, aiming at a more fundamental process rationale in particular regarding the choice of carbon precursor and mitigation of Cu sublimation. CH4 as precursor requires H2 dilution and temperatures ≥1000°C to keep the Cu surface reduced and yield a high quality, complete monolayer graphene coverage. The H2 atmosphere etches as-grown graphene, hence maintaining a balanced CH4/H2 ratio is critical. Such balance is more easily achieved at low pressure conditions, at which however Cu sublimation reaches deleterious levels. In contrast, C6H6 as precursor requires no reactive diluent and consistently gives similar graphene quality at 100-150°C lower temperatures. The lower process temperature and more robust processing conditions allow the problem of Cu sublimation to be effectively addressed. Graphene formation is not inherently self-limited to a monolayer for any of the precursors. Rather, the higher the supplied carbon chemical potential the higher the likelihood of film inhomogeneity and primary and secondary multilayer graphene nucleation. For the latter, domain boundaries of the inherently polycrystalline CVD graphene offer pathways for a continued carbon supply to the catalyst. Graphene formation is significantly affected by the Cu crystallography, i.e. the evolution of microstructure and texture of the catalyst template form an integral part of the CVD process.