What is the simplest structural unit of an element or compound?
For a solid lattice (metal, ionic solid, crystal) I would say the answer is unit cell, for a non-charged compound  that isn't a lattice (including solution/gas phase) I would say molecule, and for a charged one I would say ion-pair / ternary ion-associates / quaternary-ion associates for two / three / four ion clusters. For polymers, I would refer to the basic unit(s) being the component monomer(s).

There is, as has been identified in the comments, an issue with allotropes, Carbon (Diamond, Graphite etc) can be encompassed within 'unit cell', but for elements like phosphorus and sulfur, it's a little more complicated. There I would contend that the basic unit of e.g. P4 (white Phosphorus) is the molecule, and for the rest, I would return to referring to the unit cell, or 'monomer' in the case of amorphous networks.