Since a lot of people like to use sandpaper, I came up with this model.  It has a 6 inch glass disc, and a leather strop to fit on the top of the nut holding the disc. 34 rpm, and reversible.

     You can use the stick on discs, or some wet or dry sandpaper, and just wet the paper and it will adhere pretty well to the disc.  Easy to change grit that way.

     You will need to come up with your own sandpaper.