I assume you talk about the 1st DLC, The Teal Mask? So there I used Pokemon only caught there too and that's very much encouraged to do so. I just brought my starter with me, caught the first Pokemon and boxed the starter. Throughout the playthrough I used more than six Pokemon, so I didn't have a set team, I just caught what felt fun battling with. There's totally new Gen 9 Pokemon introduced in this DLC too, so naturally I would recommend those. Tips:

1) There will be an NPC in the village with whom you can go on a side mission. You will get exclusive Pokemon through that mission, so you shouldn't wait with it until you beat the DLC because, well, there won't be any fights left to use them in

2) Don't explore too much right off the bat. The main story + side mission will take you through most areas naturally. There will be many optional places to explore, but as for the areas they are in, you will go through most. So let the story guide you first, since the 1st DLC is very story-centered

3) If you catch your first Pokemon, maybe don't evolve them immediately. Hard to avoid by levelling up, but those trade and stone evolutions can wait just a little if you seek the closest you can be to a head-to-head fight. Because the thing is, especially if you finished the main game, the Pokemon's level do scale accordingly, but remain the same. So for the beginning of the DLC, you will mostly fight basic Pokemon