First-principles calculations were combined with scanning tunneling microscopy (STM) measurements to analyze the adsorption of diindenoperylene (DIP) molecules on Cu(111) surfaces. The influence of the substrate on the geometry of single adsorbed molecules, their diffusion barriers, as well as the role of step-edges and intermolecular interactions for molecular self-assembly and structure growth are studied. Long-range ordered arrangements of DIP molecules are found to be most favorable irrespective of the terrace width. Energetically less favored short-range order structures, however, are observed as well.