When to use evolutionary stones

The Evolution level only matters if you are holding off to get a specific moves, which in Eevee's case probably doesn't matter that much, unless you want Take Down or Double Edge.

Take a look at Eevee's and Vaporeon's learset, and see if there's anything you want to hold off evolving for.

It doesn't impact stats at all. In other words, whether you choose to evolve at level 1 or level 100, they will have the same stats if you compare them both at the same level once both are evolved (assuming IVs and EVs are the same).

In case you were wondering, the Move Reminder can help if you're in a bit of a 'Catch-22' situation.

Say you want to wait until Eevee learns Double Edge (37), but also want to evolve earlier so that Vaporeon learns Acid Armour (29). What do you do? You wait until Eevee learns Double Edge, and then evolve it. Take it to the Move Reminder, who will be able to teach it Acid Armour.

It doesn't work in the reverse scenario:

One limitation is the Move Reminder is restricted to the particular moveset associated with the Pokémon's species (i.e. current evolutionary form). Many Pokémon, especially those that evolve by way of evolutionary stone, have access to moves that their evolutions do not, such as with Eevee, who can learn Take Down by level though none of its evolutions can.

Emphasis mine. Source