Anything that is labeled 100% cotton, or 95% can work too. I guess you are either thinking thrift shop or fabric store?? At thrift shops, you can use any large cotton tees, flannel PJs, terry robes, flannel sheets, knit jersey shirts, soft denim even, flannel pillowcases, knit blankets in the baby section, receiving blankets, waffle knit like long johns, cotton fleece sweaters and pants, kitchen towels, cut up old diapers, etc. Old towels at home, and then replace with new ones.
Oh, and don't forget microfiber terry and terry towels in the auto dept, work well too. And, are soo cheap. Usually as an inner fabric, since the regular terry is cheaper, and it doesn't stay soft. The micro is soft, but I don't know how that washes.
If you are talking fabric store, terry cloth, flannel, cotton knit, knit jersey, waffle knit, bamboo (can't usually find this at brick and mortar shops), velour, cotton fleece etc. Anything cotton that has some stretch and stays soft. Kymberli