Atom-based quantum simulators have had tremendous success in tackling challenging quantum many-body problems, owing to the precise and dynamical control that they provide over the systems' parameters. They are, however, often optimized to address a specific type of problems. Here, we present the design and implementation of a $^6$Li-based quantum gas platform that provides wide-ranging capabilities and is able to address a variety of quantum many-body problems. Our two-chamber architecture relies on a robust and easy-to-implement combination of gray molasses and optical transport from a laser-cooling chamber to a glass cell with excellent optical access. There, we first create unitary Fermi superfluids in a three-dimensional axially symmetric harmonic trap and characterize them using in situ thermometry, reaching temperatures below 20 nK. This allows us to enter the deep superfluid regime with samples of extreme diluteness, where the interparticle spacing is sufficiently large for direct single-atom imaging. Secondly, we generate optical lattice potentials with triangular and honeycomb geometry in which we study diffraction of molecular Bose-Einstein condensates, and show how going beyond the Kapitza-Dirac regime allows us to unambiguously distinguish between the two geometries. With the ability to probe quantum many-body physics in both discrete and continuous space, and its suitability for bulk and single-atom imaging, our setup represents an important step towards achieving a wide-scope quantum simulator.