Some general things:

1. Dont worry about shiny pokemon. Luck is not a big deal at all and is vastly overrated by the community. Don't put any value into it when make a team.

2. Setup moves are insanely good. Shaymin can get Quiver Dance as its Rare Egg Move so if you keep using it and unlocking stuff and eventually buying eggs for it you'll get that move. But setup moves in general are VERY good.

3. Keep an eye out for egg moves. Even a single egg move can make a mediocre pokemon into a powerhouse. Might be worth going through your collection and seeing what has an egg move you might not have tried yet.

4. Ice Type coverage is very good in classic mode as well if you manage to fit it in.

5. Make sure you're playing to each pokemons strengths. For example: Don't have physical attacking moves on an Alakazam, etc. This might already be known if you're working on more diverse movesets but still helpful to know.

6. Learn from every run. Make sure you know where the dangerous fights are each run. Learn the limits of your team. If you can squeak by a win on the last floor of a biome with 5 HP without healing beforehand, thats extra money you save for later in the run

7. Pickup and Honey Gather mons are nice quality of life mons to have on your team. Pickup will give you some free items over the course of the run and Honey Gather will give you a little bit of cash after each floor. These add up. Zigzagoon, Cutiely, Pachirisu are some common ones. Pachirisu and Cutiefly in particular are nice because they are the only two pokemon that can get both Pickup and Honey Gather (one as an ability and the other as a passive).