Thanks for all of the replies.
Cotton T-shirts do a fine job for polishing, but they're not so great for my daily tasks. I need the "traditional" white shop rags, thinly-bound along the edges, for the type of work that I do (restoring ancient carburetors). The bound edge allows me to "catch" it over the end of a tiny screwdriver without tearing, douse it with carb cleaner and clean dirt out of very small bores and passages. The "face" of the rag is (obviously) used as well, but it is ineffective if it is woven thinly like cheesecloth.
And why do I specify "white" cloth? Because the dye in those red rags is rarely colorfast, and does it ever make a mess of my work and my hands! 😝
Jeff