Ok, these are the strategies I can think of:
For rental Pokemon, the best to choose is an Ice Type. Jinx is a great choice, as it has Ice Beam which I can tell from my personal experience because I've battled Zygarde before, Ice Beam does a tremendously huge amount of damage. If there is no Ice type rental Pokemon, try to get Sharpedo or Tyrantrum. Sharpedo because of Scale Shot, which is super-effective and is not weak to Dragon or Ground. You could also pick Tyrantrum because it also has Scale Shot, being super effective and increases to 130 Power when Dynamaxed. If you can't get any of that, here is the last choice I know. Pick Nidoking with Ice Punch. Ice Punch has good Power and is 4x effective.
Now, if you don't find any of those rental Pokemon, then during the adventure catch all the Pokemons you find, because you never know when they have Ice type moves or Fairy type moves. Also, choose paths that have berries in the way. They heal 1/2 of your Pokemon's max HP, so you get more health back to prepare you for the Zygarde. One common option is Liepard. Liepard has Play Rough, a powerful super-effective move that can do a lot of damage. Flygon is also good, but it is weak to Zygarde.
Sorry for the long paragraphs, those are the advice I can think of, so I hope I helped and wish you luck on catching Zygarde!