Get the book REVERSIBLE QUILTS TWO AT A TIME by Sharon Pederson. You construct the block and quilt it at the same time then put the quilt together with strips.
You might want to make the quilt out of flannel with Hobbs 80/20 cotton batting if you want ease of cleaning. I made a quilt with this combo in 1999, it gets washed weekly and it's still together and keeps everyone warm that is snuggled up with it.
Many people have tried to take that quilt because it is so cuddly warm and well used.
Good luck.