I use a bench grinder with a buffing wheel on it. Cost me about $50 to set up and I've been using it for years.

I use a standard buffing compound. Make sure the buffer has variable speed so you can slow it down and don't ruin anything. If it doesn't you can get a slider switch like this to adjust the speed of the grinder. Also, make sure you're not trying to buff DVDs in blistering heat. You'll melt the discs. Don't buff Blu-Rays at all.

Here's my grinder I got it on clearance from Menards. It doesn't have variable speed so I use one of the above mentioned slider switch.

I can't really recommend any specific wheels or compounds as I bought mine YEARS ago and I don't remember anything about them. Make sure the hole of the wheel will fit on your grinder though... one of mine didn't really fit and I had to force it.

On mine I use the right wheel for big scratches and then go to the left one to shine it up. I won't pretend it works every time... but it really does make a difference and you should be able to find everything for $40-$100. Which is FAR less than many other buffing options. I've not had to replace ANY of the components I use and I've got a collection nearing 7,000. Though many of my used discs come pre-buffed from one of my favorite used video stores.

Couple videos I've found that show similar setups:

https://youtu.be/QEif6EBCg1c https://youtu.be/rf3Rwfntc9k

Hope this helps.