I'm trying to cut or have cut about 48 (316 quality) stainless steel disks
> cut that range from 1 inch to 7 inches in diameter. The thickness would be
> about 1/16 to 1/8 inch (looking for the thinnest possible) and have a 1/4
> inch hole cut in the center. What tools would I need to do this by hand? I
If you are really looking for the thinnest possible, consider stainless steel shim stock. I used to do a lot of work with 0.006", and it comes thinner than that. Would not be especially rigid/flat for a 7" disc at that thickness, but I'm not clear how rigid/flat this needs to be from your description.
A center punch, a compass, a drill, a jeweler's saw and a file would be the bottom end tooling for thicker material. A 1/4" hole punch and aircraft shears might do for shim stock. Not clear from your description how precise these need to be (ie, should they be cleaned up in a lathe, or is that more precision than is needed?) This affects tooling needed.
PS: The reason I'm using this is to test some math theories a friend has
> and apply them to electrolysis.
If you are doing electrolysis with stainless electrodes, be aware that you may be producing/exposing yourself to really nasty chromium compound polluted waste material.