AZ, for shooting patches, the best material choice and lube can't be predicted; you pretty much have to try several samples and see what works best as you work up a load. For my last rifle, at the local JoAnn fabric store, I bought a selection of a couple of thicknesses of linen, pure cotton twill, etc,. A half yard of each was enough for several dozen shots to see what produced the best groups. The stuff that didn't work best got cut into larger squares for cleaning patches. Your punch should be right for shooting patches, but a bit small for cleaning patches.
For cleaning patches, the more material you can get down the bore without jamming up means more fouling you can bring out on each patch. In my .54, I've started using pieces of shop strength paper towels from Home Depot for the bulk of the cleaning chore. You've got to be a bit careful not to punch the jag through when starting it down the muzzle, but once started, they work just fine, and are cheaper than cloth.
SCL