By far the best thing I've tried, is a micro-fiber cloth. Check out your local car parts/junk-bling car shop as they're sold as 'detailing cloths'. They pick up finger grime and sweat much better and quicker than cotton, and they definitely don't scratch. Once I started to play basses in the $2K+ range I got a bit picky about what I used on them...and these don't leave any of that super-fine spider-web scratching that other cloths can leave. I was a bit leery at first, as they don't feel as soft as cotton, but I'm completely sold, and even give them away to guitar playing friends. I also use one to clean my glasses, and have had no problems in over a year...so it must be pretty non-abrasive!
I breed my own silk worms and weeve bass clothes that I throw away when I'm half way through cleaning my bass. Or just anything soft and lint free.
As to whether or not to be very particular about the material used, did you ever wonder why all those fine swirl marks miraculously appear all over your basses?
I rarely clean my bass (much like my truck and my house). But when I do, I use rags made from clothes thad don't fit, regardless of the material. I have never noticed fine swirl marks, but now I'm curious so I will have to check. A chamois seems like a good idea, since it is not supposed to scratch paint. But based on the above testimony, I'm going to give the "micro-fibre" cloth a shot.
Yup. I have used chamois on all my instruments since about 1964. Don't know if it's any better than anything else, but there's something about using a chamois that feels right. I keep mine in a sealable plastic bag in my bass case. After I use it, it goes into the baggie, I breathe into the bag to give a little moisture so it doesn't dry out, then seal it up. Once every couple of years I clean the chamois. I buy the best chamois I can get regardless of price - it lasts forever if cared for.
+3 on micro-fiber. I carry one with me in my gig bag and leave one at home. They don't leave the tiny surface scratches like the fibers of cloth do.