We have combined heat capacity, vapor pressure and thermal resistance measurements to characterize layering and onsets of superfluidity on a highly uniform graphite substrate, UCAR-ZYX. Strong desorption heat capacity peaks correspond to individual atomic layers "stripping off" the substrate as T is raised. These are used to find layer capacities, which in turn allow a precise layer determination for our thermal resistance data. Precursors to superfluidity and evidence for 3D liquid puddling are compatible with percolation models of superfluid onset for helium films thicker than about 5 atomic layers