I always keep it with me, I usually base my team around my starter with types and stuff.
I love the starters because they have been with you from the start, so they have a special sort of relationship with the trainer.
once I got my porygon from my pearl version(that's right I have both versions and porygon z is my signature wi fi pokemon) I kicked my starter into a ditch and left it to die(I hate you piplup!)