The idea behind fishless cycling is that you have grown more than enough bacteria to remove all the ammonia and nitrite from a sensibly stocked tank of fish. But cycling does not grow all the other micro-organisms that a mature tank has. A mature tank is generally considered to be one that has been running trouble free for at least 6 months, by which time all the other micro-organisms have grown.
Some species of fish do better in a mature tank, so these should be left for a few months. Neon tetras spring to mind here - they used to be hardy fish and you'll still see them recommended as such but intensive breeding has made them more sensitive.
Cories need sand - do you have that?
The best website for researching a species is Seriously Fish
https://www.seriouslyfish.com/knowledge-base/ This one is written by experts; other sites are written by people with less knowledge. Make note of the hardness the fish need; the tank size they need and make sure all the fish you choose have the same temperature range.
(Most rainbowfish need hard water so research before buying to make sure you don't get any hard water species)