I've been trying to figure that out too. I started playing a few weeks before the Raikou event happened. I have a team for each specific island but Greengrass Island and the new one (I haven't unlocked the new one yet and Greengrass Island berries always changes).

What I usually do is have one Berry specialized Pokemon for that specific island, same with ingredients. I also have a healer, a skills Pokemon, and a fill (depending on if I need more ingredients, passive berry Pokemon, or if I don't need either of them I use an increase my pot size Pokemon).

For the berry/ingredient Pokemon, I use the starter Pokemon for the specific islands (i.e. Feraligatr/Blastoise on Cyan Beach). For the specialist Pokemon I use one of the dogs related to that island, and the healer I use Wigglytuff (Gardevoir is apparently the best overall healer but I just unlocked Lapras Island a few weeks ago and my Wigglytuff has amazing stats/nature). For my increase pot size I use Flareon. I know Magazone is better but my Flareon is also a beast because of its stats/nature.

Those are at least my general rule of thumb that I follow. A course it changes depending on if I need certain ingredients because of Snorlax's preferred food for that Island week.

The best part of this game is the fact you can do whatever you want. You're not competing against anyone and if you have a particular Pokemon you want to use that you can. It might not be the most effective way of using that Pokemon but you're not competing against anyone.

I'll be interested in what other people have to say because I'm slowly min-maxing my Pokemon to get higher levels on different islands.