We show that the strength of correlations, as controlled by the charge-transfer energy, is a key chemical parameter tuning superconductivity across the hole-doped cuprate families. Using first-principles calculations, we extract two essential microscopic parameters, the charge-transfer energy and the inter-cell oxygen-oxygen hopping, which correlate with the maximum superconducting transition temperature. Exploring the superconducting state in the three-band model of the copper-oxygen planes using cluster Dynamical Mean-Field Theory, we find that variations in the charge-transfer energy largely accounts for the trend in Tc across the cuprate families.  With this framework, we analyze recently synthesized square-planar nickel compounds and discuss the possibility of superconductivity in these materials.