This assumes you don't want to use a master ball, and you're trying to catch the Faraway Island Mew, because that's the only place with wild Mews.
If both assumptions are true, then the best ball would be the net ball. The key here is that, when Mew transforms, it copies the target's types and catch rate. The easiest way to catch Mew is to use a water or bug Pokemon with 255 catch rate (guaranteed catch with net balls), or one of these: Caterpie, Weedle, Poliwag, Magikarp, Ledyba, Spinarak, Wooper, Wurmple, Lotad, Nincada, Feebas, Spheal, Clamperl Use it to battle the Mew, and throw a net ball after the Mew transforms, so you'll get a guaranteed catch. If the Pokemon faints before the Mew transforms, simply soft-reset.