I'd just kinda float around, visiting the people in different towns. I don't think that I'd really challenge any contests or gyms unless somebody I was with wanted to/suggested that I do.
I'd probably just catch Pokemon that I befriended instead of going after Pokemon.
And I would probably just carry around the most recent Pokemon I had.
But I'd try to convince my Pokemon Professor if I could have a Pichu or Ghastly for a starter... Because I'd like to have those around me.
But if I had decided to fight the Elite Four, or some big important battle/event like that , I'd probably try to have...