Being an avid shiny collector I have to put them into shiny and non shiny category
Overall my favourite is Espeon. I had one in my original silver which i did not evolve until it had learned bite as an Eevee. I didn't think about the whole physical/special differences back then so it was a pretty baller Espeon! It sweeped Sabrina with that bite it had. =3
It also reminds me of the Dash card from Cardcaptor Sakura which was one of my favourite cards. Plus I love purple and favour the psychic type in older gens.
In terms of shiny, Espeon is not my favourite, Umbreon is. I love the contrast of the black and blue, it's simply beautiful! I also love shiny Eevee, it's so pretty!
Coming second would be Jolteon, SO fast and so very useful when I used one in a playthrough of LG.
I also love Flareon. I don't care about it's lack of good moves. My one was useful and the shiny is lovely!
Vaporeon, also highly effective and has a great shiny.
I've not used the other two in gameplay yet. Overall their design is less appealing but I know they have their strengths. Shiny Glaceon is also beautiful.