I obtained Eevee, and I did evolve him. My choice was a Flareon. I just liked Flareon's design the most of the three Kanto eeveelutions, even though Vaporeon and Jolteon are stronger, particularly in the debut generation, the warm red color scheme of it's fox fur color, big, shiny dark eyes and flowing, bushy told mane endeared me more to him.
Flareon didn't see a whole lot of action on my first playthrough of Pokemon Yellow, one reason was because I took the gift Charmander (and all the other Kanto starters) earlier, so I had a Charmeleon by that point in the game, but I believe I did still bring Flareon with me to Erika's gym. One time I also used Flareon on a mono fire type play.