I would sink wash "really dirty" discs, and then if desired use a cleaning machine.
I use the label protector noted in the following link and warm filtered water ran through an old WaterPik.
Always thoroughly rinse prior to applying any brush/cloth to avoid scratching.
I also use a DIY wash solution and various brushes/micro fiber towels along with a drying rack.
The filtered water from our kitchen faucet has no noticeable residue (when evaporated) unlike the distilled water I have purchased from local supers.
DeKay