We use a variational approach to gain insight into the strongly correlated d-wave superconducting state of the high Tc cuprates. We show that Mott physics leads to qualitatively different trends in pairing and phase coherence: the pairing scale decreases monotonically with hole doping x while the SC order parameter shows a non-monotonic ``dome''. We obtain detailed results for the doping-dependence of a large number of experimentally observable quantities including the Fermi surface, nodal quasiparticles, energy gap, optical spectral weight, and superfluid density. Our results are either in remarkable semi-quantitative agreement with existing data or have been subsequently verified. At small hole doping we discuss the tendencies toward various competing orders including antiferromagnetism. Finally we discuss sum rules for one-particle spectroscopies, which shed light on the striking asymmetry in the tunneling spectra in doped Mott insulators, which are useful in estimating the local doping variations in inhomogeneous materials.