If you have access to a muture filter can you not get some of the media from it? It'll be far better than just washing it out in your tank.
In theory, you should be able to stock a few small fish immediatly after putting mature media in, but I prefer to qualify it for a few days with either some household ammonia if you have any, or by letting a pinch of fish food break down until I have an ammonia reading, adding the mature media, and then testing to see if the ammonia has gone by the next morning. Hope that makes sense.
I'd never recommend neons for a new tank, even if the filter is fully cycled. I don't know why, but they just don't do well. I don't even quarantine mine anymore; I just lose too many, even with mature filter, gravel, plants and rocks taken from well established tanks. Better off waiting a few months rather than lose them.
