You can use sweatshirts. They can be mixed in with any other type of material that is machine washable. When the quilt is finished, it is difficult to know if a block was from a T-shirt or a sweatshirt.
Most mom's will save out a few or all their children's baby clothes. They are just too important to give away. You can use baby clothes in a T-shirt quilt or have a quilt made just from baby clothes. Read more about baby clothes here.
Andrea Funk is the inventor of T-shirt quilts made with multiple blocks sizes. The modern method of making T-shirt quilts. In 1992 she founded Too Cool T-shirt Quilts. Her life has been immersed in T-shirt quilts ever since.