Before transport data can be understood quantitatively, a few prerequisites have to be fulfilled: the geometric and the electronic structures of the metal/molecule contacts have to be known, and electron correlation effects have to be taken into account. Here we discuss experimental and theoretical approaches to tackle these challenges. On the theoretical side, density-functional theory (including van der Waals-corrections for structural optimization) is combined with many-body perturbation theory and numerical renormalization group theory in order to include all relevant correlation effects. We had already discussed such features in a previous study [Phys. Rev. B 84, 125413 (2011)], but some remaining differences between our calculated spectra and our experimental data from a scanning-tunnelling microscope remained unexplained. Here we show that the explicit incorporation of van der Waals interaction in the calculations, that had been negleted before, yields improved geometric structure and leads to much better agreement with our measured spectra. This clearly demonstrates the significant sensitivity of electronic transport to structural details.PTCDA molecule in a junction between a silver surface and an STM tip.