I actually wrote a fanfic on my own pokemon story (never get to finish it however). The region setting is Italy themed with greek mythology influence. The protagonist starts out in a small town called "Eevillage"(Lame I know but I was only 15 at that time) because it is the perfect habitat for eevee and therefore a lot of wild eevee can be found here. One of the tradition is that every year there is an exam that invite trainers from all over the world as examiners to determine whether the contestants (from the village) are ready to become a pokemon trainer. The contestants must use at least one eevee (non evolution, in fact all the eevee that you keep are supposed to be holding everstone until you become an official trainer). From the beginning, the player is going to start with some small quests in the village before the exam to allow them to catch and train other pokemon as well. On that day, right after the protagonist passed his/her test, a group of Team Genesis' grunt break in with a weird weapon that can siphon energy from pokemon that evolve using elemental stone and force them to devolve(ie, starmie turn back into staryu). For those that evolve naturally,they would be weaken and unable to fight as well. But as mentioned, this exam has trainers from many places, one of them is a Dark type gym leader, Hades. He identified the leader of this operation and asks the protagonist to distract the other grunts while he battle with the leader. It was a quick fight because he used weavile to hold the leader hostage and force the rest of Team Genesis to back down. After the incident, our protagonist finally received his/her own trainer card and pokedex to start his journey. Before leaving, the protagonist will be asked which eevolution they desired for his/her eevee and will be given the corresponding stone (Umbreon, Espeon and Sylveon will still evolve by normal means but player will still receive Dust, Dawn and Shiny stone, but leafeon and glaceon evolve by holding leaf and ice stone). Along the journey to battle the 12 gym leaders (each corresponding to 12 zodiacs), elite four and champion, of course the player will interfere in Team Genesis' business and stop their evil plan. After the 4th gym, Pokemon Professor give the player the chance to choose a pokemon that are capable of mega evolution (excluding legendaries). There are 2 major rivals for the player, a childhood friend who is determined to become an electric type gym leader like her father once was; another rival is also your childhood friend but abducted by Team Genesis for his psychic power since young. Now he just wants to become the next boss of Team Genesis but you keep standing in his way.
Addition: each evolved eevee can learn a signature move that represent their type (Umbreon: Dark Ring, the glowing markings absorb the energy around to heal 1/4 of the hp while blinding the opponent thus reduce opponent's accuracy. Jolteon: Blitz Attack, electric version of quick attack, Espeon: Psychic Impact, deals damage and lower opponent's highest stat excluding HP by one stage, etc etc).