Some people don't like the microfiber towels. Guess it's just personal taste. I've used them for a long time now and feel they are better for the finish than the cotton.
Cotton and Microfiber both have good quality and bad quality. For the cotton towels, make sure the tag says 100% Cotton "Made in the USA". If it doesn't say "made in the USA" then don't buy it. Oversea's towels will say 100% cotton, but will still have some different materials mixed in them. Make sure it's thick and plush. Fold it over 4 times, and wipe lightly.
Microfiber towels are almost the same thing. Just buy them from a reputable dealer like Meguiars or someone like that. The ones from Target and Walmart are good for interiors, but I wouldn't touch them on my paints surface.
And like slow99 says, always inspect you towels before you put them on your car. If there is anything at all on them, either wash them or toss them in the trash.