Why are 'table salt and sugar are both terrible candidates for recrystallization'?
The solubility of $\ce{NaCl}$ has very poor temperature dependency. If you dissolve it at $100^\circ\rm C$ and precipitate at $20^\circ\rm C$, you'll essentially lose about 35 g to purify 3 g. Even using a fridge, you'll still lose more than half of the product, which is quite a bad business. Industrial process relies on evaporation, I think.

Sugar is another story. It does have a nice temperature dependence, but it dissolves too well, even when cold. Just imagine dealing with that awfully viscous syrup, like molasses. It would take forever to filter, and quite a while to crystallize. Industry can handle that, but for home chemistry I'd suggest something more pleasant.