Wow, that must have been really helpful. Well, before you jump on me, here are things you should consider:
Nature of your Pokemon: When using a Pokemon in competitive battling, a good nature means a 10% gain (or loss) of a stat. While this isn't all that important in-game, it does make an impact in meta-battles.
Type of Pokemon you intend to use: If you already have too many Physical attackers, go with the Special variants, and vice versa. A good team consists of a good proportion of Attackers to deal with various threats.
Other team-mates: While this does not mandate your final decision, it is important to remember that certain Pokemon work well with others, be it in terms of effective neutral coverage, or resisting each other's weakness(es).
Others: Un-important, but be sure to know how each Pokemon looks like in the evolved form. Some Eeveelutions look weird, in the sense, a color palate that makes it somewhat unappealing. If you want the full effect of your Shiny Pokemon, make it evolve into an Eeveelution whose color isn't barely noticeable, or distracting-ly bizzare. Apart from that there are also IV's. Check to see which IV's are better than the rest, an try to utilize this to the best effect possible.
Now the Pokemon themselves:
Flareon is a good Physical Fire type, but it lacks a strong movepool or even a diverse one at that. Flare Blitz and Facade are literally the only worthwhile moves.
Leafeon is excellent getting access to STAB Leaf Blade, Swords Dance, Synthesis and X-Scissor. Effective neutral damage. Worth considering.
Albeit looking very weird, Espeon is a force to be reckoned with. Strong Psychic and Fairy type moves at its disposal, and excellent Special Attack and Speed, this is quite an excellent choice with a high recommendation from me. I just hope you like this unholy shade of green.
A speedy Special attacker with decent movepool, there is hardly a Pokemon out there to outspeed this Thunder Kitty. Use with caution, though, because this bad boy is frail.
Specially defensive, but with a STAB 1.3x powered Hyper Voice and a fairly decent Special Attack, this Fairy can be a massive asset to your team.
A highly effective physical tank, Vaporeon can melt into the battle and stall excellently.
A favourite of many, with cool glowing rings, Umbreon is the Eeveelution that mattered in the past when it came to stalling. Sadly pushed back by the introduction of the Fairy types, this thing is still a good choice.
An Ice type with decent Special stats. Can be used somewhat as a Specially defensive Pokemon, but Ice is a bad typing for defense in general. Better stick to Ice Beam + Shadow Ball combos. Still a good addition on Hail teams, though.