To throw another complication into this discussion, when I get a new fish, I use the Tank Transfer Method. Basically moving the fish from one tank to another every 72 hours to escape ich. It’s worked very well for me with all my additions.
For TTM, you don’t cycle at all, you just monitor the ammonia, and the fish gets moved before it gets too high. No Copper is used, but I dose PraziPro in two of the tanks for flukes etc. Do a search on that method and there’s some really great threads. I like it because I don’t have to test for copper or deal with the addition, and when done right, I think its less stressful on the fish...
When I get to the last tank however, the fish stays there for an observation period so I can be sure there’s no other parasites. In this tank, I use a lot of bio filtration: a hang on back filter with sponge and carbon, and a sponge filter. To seed the tank with bacteria, I use a bunch of MarinePure balls that have been sitting in my sump for a while and fully colonized.