This is my opinion (Using gen 6 movesets because you said you were doing this in X)
Vaporeon: Level 16. After one level up, you receive Water Pulse which is 20 power higher then Water Gun, and with a confusion chance. Plus, 4 levels later you receive Aurora Beam, which can provide coverage against Ramos. Later on, it can learn Surf by HM, giving it it's strongest STAB move and you one less need for a HM workload. If we're talking coverage it lacks in that department when it comes to facing Electric Types, Grass Types can be dealt with by Ice Beam or Aurora Beam but Vaporeon's only move that's good against Electric Types is the physical move Dig, by TM which isn't good for the special attacking Vaporeon.
Jolteon: If I had to give you a proper answer to this, it'd be level 8, By level up, Jolteon only learns three special electric type moves. Thunder Shock, which is weak and Discharge, which is decently strong but is learnt at level 37 in X/Y! You can also count Thunder, but we all know how inaccurate that move is when there's no rain. + learnt late. (Yes, there's also Thunder Wave, but that's a status move) And TMS don't even help, Thunderbolt is after you beat Clemont, Charge Beam is only 40 power and found on route 13 and Volt Switch is in the battle maison!,
Flareon: if I had to give you a proper answer, level 19. One level after, it learns Fire Fang which uses it's superior physical attacker (Unless you wanna use it's weaker Ember). Level 47 gives you Flare Blitz but that does recoil. And that's it! All it's STAB Fire TM moves are special. If you're set on using it, teach it Rock Smash. It helps with rock types.
Espeon: Level 8 (Again). Learns Confusion at level 9 and that'll be your STAB until level 20, where you get the (slightly better) Psybeam. Though, you'll be stuck with that for STAB until level 37, unless you want to use the two-turn Future Sight, which it gets at level 25. Once you hit Terminus Cave, you can get the TM for Shadow Ball for coverage against Ghost and Fellow Psychic types. Once you beat Olympia and Valerie, you get the TM's for Calm Mind and Dazzling Gleam respectively, the latter being helpful for coverage against Dark Types
Umbreon: Since it's more bulk focused, I say evolve it at level 16. It gains Confuse Ray at level 17 then at level 20, it gains Feint Attack. You can find the Rest TM pretty early, in Cyllage City, to make use of it's bulk. Also, Toxic can be found on Route 14, if you like stall.
Leafeon:It's only physical attacking moves via level up are Razor Leaf at level 9 and Leaf Blade at level 47! And like Jolteon and Flareon before it, TMS don't help. Because all STAB Grass Moves it gets by TM are special! Though, if you're set on using it, go for level 28, it gains Swords Dance at level 29 which can pair well with Leaf Blade (When you eventually get it). Plus unlike Vaporeon, it can take advantage of the Dig TM because Dig uses it's physical attack, adding coverage against Fire-types.
Glaceon: If you want to trudge through with a Eevee until you reach the Ice Rock. Like it's counterpart from Sinnoh, it only learns two ice special STAB moves by level up. Icy Wind at level 9 and Blizzard at level 45 but that's inaccurate. Unlike Leafeon, though, it does get good TM choices like Frost Breath (which is located in the same cave the ice rock is) and Ice Beam. (After you beat Wulfric) As a default, go for level 8.
Sylveon: Level 19. It gains Draining Kiss at level 20, which also recovers HP making it better then Fairy Wind. Though you'll be stuck with that for STAB for 13 levels until you reach Moonblast. Once you reach Pokémon Village, you'll get the Psyshock TM for coverage against Poison types
TLDR:
Vaporeon -16
Jolteon-8
Flareon-19
Espeon- 8
Umbreon-16
Leafeon-28
Glaceon-8
Sylveon-19