This paper considers the dynamics of the scattering of planetesimals or planetary embryos by a planet on a circumstellar orbit. We classify six regions in the planet's mass versus semimajor axis parameter space according to the dominant outcome for scattered objects: ejected, accreted, remaining, escaping, Oort Cloud, and depleted Oort Cloud. We use these outcomes to consider which planetary system architectures maximize the observability of specific signatures, given that signatures should be detected first around systems with optimal architectures (if such systems exist in nature). Giant impact debris is most readily detectable for 0.1–10 M⊕ planets at 1–5 au, depending on the detection method and spectral type. While A stars have putative giant impact debris at 4–6 au consistent with this sweet spot, that of FGK stars is typically ≪1 au contrary to expectations; an absence of 1–3 au giant impact debris could indicate a low frequency of terrestrial planets there. Three principles maximize the cometary influx from exo-Kuiper belts: a chain of closely separated planets interior to the belt, none of which is a Jupiter-like ejector; planet masses not increasing strongly with distance (for a net inward torque on comets); and ongoing replenishment of comets, possibly by embedded low-mass planets. A high Oort Cloud comet influx requires no ejectors and architectures that maximize the Oort Cloud population. Cold debris discs are usually considered classical Kuiper belt analogues. Here we consider the possibility of detecting scattered disc analogues, which could be betrayed by a broad radial profile and lack of small grains, as well as spherical 100–1000 au mini-Oort Clouds. Some implications for escaping planets around young stars, detached planets akin to Sedna, and the formation of super-Earths are also discussed. ; Other ; MCW, AB, and AS acknowledge the support of the European Union through European Research Council grant number 279973. APJ acknowledges support from NASA grant NNX16AI31G. AS is partially supported by funding from the Center for Exoplanets and Habitable Worlds. The Center for Exoplanets and Habitable Worlds is supported by the Pennsylvania State University, the Eberly College of Science, and the Pennsylvania Space Grant Consortium. This research has made use of the NASA Exoplanet Archive, which is operated by the California Institute of Technology, under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Program.