Need to clean some cds

I'll second the Meguiars "Scratch X".
I have had great success with it.
The best cloth to use is a BRAND NEW baby diaper.
Doesn't get any softer that that.
I use them on my classic car.
Just my $.02.
Rick.

Do you wipe from center to edge of each CD (or in circular motion as with vinyl record) when rubbing out scratches on a CD?

Power tools, you need power tools my friend.
Seriously, doing anything to the CD's will only make them sound worse. Polishing one area will made the surface wavy- not a good thing. And any scratch removing polish will put in zillions of finer scratches.
You could try Novus #1 which puts a shine on CD's. Or Armor All. Just make sure you wipe off the excess so it doesn't spray around the inside of your CDP. Also clean the center ring area of the CD. I use saliva since it's plentiful and easily accessible. Otherwise the disc may slip due to the slippery surface oils and not drive correctly.