Oh, I think about this situation all the time. In the Pokemon World, I would likely not have all that many Pokemon on me. Wouldn't be able to handle collecting so many and giving them all attention. Instead of carrying six, I'd probably only carry two or three on-hand. It's more realistic that way. All of these creatures are living beings, and they require love, attention, and food.
Also, whilst I'd occasionally battle for fun and sport, it wouldn't be my main focus. I've seen in the anime and such that many people use Pokemon in their jobs. I would likely work as a kind of administrator/manager of something. Perhaps the head of the Gym Quality Inspection Team for the Pokemon League. And it would be my job to travel around the world for these inspections, with my Braixen, Espeon, and Flygon. The first two would help me with the inspections, using their Psychic abilities. The last one would mainly be for travel purposes.
I would also be an artist on the side, using my Braixen to help me with my pieces. I'd probably cover her stick with paint and collaborate with her.
It would be perfect for me. Whilst I enjoy doing art in real life and want it to be my job, I would much prefer a job that involves more importance, managing and enforcing standards. Something practical so I could feel like I'm doing things. And I could still have my art be an important part of me and as something I do for fun/to express myself.
This is just a thought. I don't really have a full idea of what I'd do in the Pokemon World. But it seems most likely.