You should use your Water Stone when you are sure that you got all the right moves for Vaporeon when it evolves from Eevee. When Eevee evolves into Vaporeon, it may leave some moves out that you are unable to learn. This is called Pre-Evolution moves. Some Pre-Evolution moves of Eevee include: Take Down, Baton Pass, Trump Card, and Growl. When your Eevee evolves, it is unable to learn these moves anymore.
So, if you do not want any of these moves to be included to your Vaporeon via level up, I suggest you use the Water Stone right now because Vaporeon is a strong Pokemon to use in battle rather than Eevee.
If you evolve Vaporeon and leave some moves out at a lower level, you can remember it via heart scale at the Move Maniac at Pastoria City.