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On my first run through any new gen, I limit myself to only using new pokemon.
>Something in the middle
I run through the game until I see pokemon that I want to use. Unless it's a first run, I generally don't catch pokemon I don't intend to use. As a result, I go through the majority of the game with 3-4 pokemon.
>HM Slaves
With the exception of moves that are somewhat useful in battle (Surf, Waterfall, Strength, Fly) I use an HM mule. Usually Zigzagoon.
>catch things as you go but don't go out of your way for it
Like I said, only on my first couple runs do I bother catching all the pokemon I can. Then I only get serious about filling the pokedex in the endgame.
>use only pokemon you can get on that cart
With only some exceptions.
>Set
It's a children's game. I also play with EXP share off.