using the lesser quality fabric in the center of your squares would work; being a lower quality it will fray well. use the best you can afford for the outsides. and make them big enough for kids over 3 years old...younger than that is a definite choking hazard. you do not want to be tracked down some time down the road to be informed your 'baby-quilt' was the cause of loosing baby!
rag quilts are NOT FOR BABIES!