I'd stick with being a trainer. I love to travel, see new things, meet new people, etc. It sounds like the perfect life for me.
A Gym Leader would be respected, but they're pretty much tied to their gyms. I'd hate to be stuck somewhere all of the time. Sure, you'd get to battle a lot and would get a good name for yourself, but it's not really my thing.
An Elite 4 member would be essentially the same thing. You'd be obliged to do things at certain times.
A Professor/Researcher isn't me at all. I hate reading and studying. Also, you'd be limited to battling at certain times.
A Breeder could be quite interesting. You'd see a lot of Pokémon and get to care for them. There would be a lot of variety. Egg hatching could be an interesting job too. This would probably be my second choice.
A Co-ordinator or whatever you call them would be a little different. To an extent, it involves a lot of what a trainer does. Travelling, obtaining ribbons (which is like badges), training, learning new attacks, etc. The thrill of battling isn't there though, and it seems a bit too formal for me.
So on that note, trainer it is. :3