We enumerate all minimal energy packings (MEPs) for small single linear and ring polymers composed of spherical monomers with contact attractions and hard-core repulsions and compare them to corresponding results for monomer packings. We define and identify "dividing surfaces" in polymer packings, which reduce the number of arrangements that satisfy hard-sphere and covalent-bond constraints. Compared to monomer MEPs, polymer MEPs favor intermediate structural symmetry. We also examine the packing-preparation dependence for longer single chains using molecular dynamics simulations. For slow temperature quenches, chains form crystallites with close-packed cores. As the quench rate increases, the core size decreases and the exterior becomes more disordered. By examining the contact number, we connect the suppression of crystallization to the onset of isostaticity in disordered packings.