If you went with this plan my feeling would be that in terms of introduction order and time the Rummys and/or Corys (depending on species) would be fine to be worked in first, dragging out the time and waiting as long as possible prior to starting any of the neon/cardinal introductions since they like a 6 month or so mature tank.
I agree that 6 is about minimum for all 3 of these types with any numbers beyond this just making things better and better, although adding numbers to the neons will add least to the bioload, whereas the rummys will eventually get a bit bigger. All 3 types will like the greater numbers but I'd probably give priority to adding more to the rummys and neons as I'd picture the corys doing ok at six.
~~waterdrop~~