Using density functional calculations, we address the energetics of the interface between the SiC(0001) substrate and the first covalently bonded epitaxial graphene layer. We consider a 6 root 3 x 6 root 3R30 degrees geometry showing the experimental periodicity, a simplified root 3 x root 3R30 degrees geometry presenting a strained graphene layer, and an almost commensurate 4 x 4 geometry where SiC and graphene have the same orientation. The total energies of the structurally relaxed interface systems indicate that the 6 root 3 x 6 root 3R30 degrees geometry is the most stable, in agreement with its experimental occurrence. The binding energy is found to correlate with the vertical spread of the C atoms in the graphene layer, with a larger extension corresponding to a higher binding energy. For the 6 root 3 x 6 root 3R30 degrees geometry, the height variation of the graphene layer displays the experimentally observed modulation with an apparent 6 x 6 periodicity. The charge transfer also correlates with the height of the graphene atoms, being more significant in graphene regions which are strongly attached to the SiC substrate.