Well, most stone-evolved Pokémon stop learning moves the minute they evolve, so it's better to hold off until they learn all their moves from their earliest stage.

It's a little bit different with Eevees, though. If you hold off on evolving them, nothing's stopping them from learning their evolved form's early moves the second they evolve, but you also run the risk of having them evolve into an Espeon or Umbreon unless you're careful.

[He'll wait before he brings up those rather large movepools. No need to bog her down with too much at once.]