What is the best variety of ADCs to learn?

would give you a pretty good variety of ADCs

1 Utility, 1 that uses Triforce for mid game power, and 1 late-game hyper carry.

Maybe someone like vayne who is mechanically important and is a hyper carry late game, Ez or Kog for triforce and mixed damage and Lucian/Cait or Jinx for Scaling damage?

I would say get vayne as a hyper-carry/"i need to cut down tanks this game" and then maybe Graves for when you need to be a total lane bully and shut down that hyper carry and finaly either Siver maybe for when you team just need the utility of reliable engage and wave clear.