I don't spend much for backings on a donation or play quilts and I won't use cheaply made fabric. A man's 3x quality cotton shirt will make a backing for a baby quilt. I find these all the time for a few dollars at thrift shops.. Need a bigger backing use four shirts and piece one. There is no excuse to use crap fabric for a quilt to give a person that has nothing.
Teens love the rag quilts. They are easy to make and are very durable using quality cotton shirts and left over fabric. I have the large rag die and a Go. I cut batting with the 6 1/2" square die, sew two ten inch squares together with batting in-between. Sew an X in the block and then run the block through the 8 1/2 rag die. . Overlap the edges and sew a row then the rows together. I can do a large size throw for a teen in less then a day.