@Andrej I don’t usually clean parts in bulk after purchase, but I do wash individual sets I sell. I put the parts in water with dish soap for a little while, then I move them to a colander for rinsing where I brush the largest plates that are more susceptible to collect dust and grime, then I rinse and shake the parts to remove as much water as possible, and finally I spread them on a towel for drying using a table fan to speed the process up.
The rare times I did clean parts right after purchase, I do the same process minus the individual brushing in my bathtub instead of my kitchen sink.