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I always run with the regional rodent as my starter. If you can't get it right away I just pretend I'm running an errand for the professor with one of his Pokémon turn I run out catch the rodent and box the stater.
Bibarel, Linoone and A-Raticate with Hustle are the best. Non-HA Diggersby is probably the last fun to use, and Gumshoos is the weakest.
I used A-Raticate in Moon and Gumshoos in Sun. I only do it once but I never have a starter in my E4 team anymore.