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I have a bit over 2 boxes, all bred to fullfill my arguably dumb case of balltism. Personally, I pick what pokéball goes with what pokémon based on a few factors:
Would it fit into any specific core?
What role does it play?
What would it look good with?
A specific factor might sometimes overthrow the other playing factors. For example, at first I thought about giving Amoonguss an ordinary pokéball or a Premier ball, but since it's somewhat consistent to put into a Fire - Water - Grass core, I decided to go with Nest Ball.
Then there are times, where I pick a pokémon based on what role it plays, as the main reason for my pokéball choice. That could be such as my Jumpluff and Dusclops, both in Premier ball. While the Premier ball looks dashing with Dusclops (to contrast with its eye, while it's grey body is still the dominating color) and Jumpluff, it's also picked because it's usually what I shove my support pokémon into. That, Dream or Heal Ball, that is.
Other times, I can pick it solely on what looks good with what. This is also usually the main factor I rely on, when picking my desired pokéball. Good examples of that case would be Manectric and Cofagrigus, which both in Quick ball. Or Timer ball Escavalier. Or Ultra ball Aegislash.