Without any sort of knowledge of what the story is about, how can we help you pick out a Pokemon to use as a character? Okay, maybe you want someone to say "Write me a story about a Mew!" and you'll write a story about a Mew. But why do you have to wait for someone to tell you what Pokemon to write about?
Alter Ego showed you one way to create a fanfiction: take a message that you want to say and then figure out what character you want to use. There is another way that I find useful, especially when working with Pokemon.
The idea is that you take a Pokemon, let's say...Lucario, because we all like Lucario. Now, if I wanted to, I could write a story about a Lucario that didn't like to fight or something but was forced to because of its family. Bam! You got a story idea of a Lucario that doesn't like to fight, so the message you can convey with your story is to follow your own dreams. It's an idea done many times before, but it shows you what I mean.
Look, just write your story. Write about whatever Pokemon you want to. You'll feel better because it's your story, and not what someone else tells you to write.
Just keep in mind that if you want to post your story, make sure that your grammar and spelling are pretty much top-notch. Look at the two threads Alter Ego linked in his post. They are helpful to writers.