I have cycled many tanks and have never had "sick fish" I would set up the tank and let the water and temp equalize then put your cycle fish in. Cheap danois are a good idea or even feeder goldfish
When I setup a new tank I use cycled filter media and substrate from my other "matured" tanks. Fill new tank about 50% with water from my matured tanks and then treat the other 50% with prime. So it's basically just like doing a large water change. I have never lost a fish with this method. I realize this will only work for people with multiple tanks. But most of us MFKRS do.