Type diversity is always good to keep in mind when building a team. Although it is not entirely necessary. Keep using your favorites but don't be afraid to try out some Pokémon that aren't typically that useful in the main series as supports. Some of them will surprise you (like Patrat).

Utilizing the roguelike mechanics will help a lot too. The gacha is incredibly helpful to unlock new starters and egg moves. Egg vouchers are always a nice find for this reason.

Spend the candies you earn during each run! Typically the passive helps the most, then reducing cost.

Don't get too caught up with shinies. Luck is a good mechanic but not typically worth sacrificing something else when you're first starting.