I vote for the kitchen cotton stuff too, I just made a dish rag with some natural color I have and washed it and it is incredibly soft. I love it! I made the rag first so I could see how soft it would get after it was washed so I could decide whether or not to make something for dd with it. Maybe the lack of dye would help the cotton to be softer? All the rags I have had have been light or natural colors and they have been very soft, some of my favorite kitchen rags.
I just got an order in of knitpicks crayon yarn and it is wonderful too. I am making a baby sweater out of it but only just started or I would post a picture. It seemed reasonably priced to me but I am not sure what your price range is. The cotton I got some time ago on a 1 lb. cone, it is Peaches and Creme brand.
I hope some of that helps!