I just inherited 800-1000 CD's and a lot of them are filthy

I use a car fine polish. Meguiars Scratch X to polish CDs and DVDs.I use VIVA paper towels. Sadly Viva now makes cheap ones too. Use only the wide smooth version. The imprinted with a textured pattern are not any good, nor are the narrower tear off sheets as good. Only the plain wide tear off sheets are really the best. (like cloth)Washing first is a good idea. If you have thousands, perhaps investing in a CD polishing machine? All the used stores seem to have versions of CD polishing machines.

curiousjim,

Use paper towels at your own risk. Cloth is best! I bet you're glad you saved those old tee shirts.

Microfiber is absolutely the way to go.  Avoid paper towels, tee-shirts, tea towels, cotton, linen, etc.  I learnt the hard way with previous pairs of spectacles.  A couple of large microfiber cloths are inexpensive, they dry easily, and they are washable.

Wash them with dishsoap. If alot of them are scratched badly and it’s worth it to you to save them a two wheeled bench grinder, two jeweler’s buffing wheels and compound works wonders. You have to be careful or you will burn them with too much pressure.

Costco eyeglass cleaner and microfiber drying towels. Cheap and easy.