I haven't used Minky but I do use fleece as a backing on almost all my quilts and never have a problem. I pin baste and use a lighter pressure on my presser foot so as not to drag. Although fleece is stretchy, it's not that bad and with good basting it behaves well. I do not use batting in my fleece backed quilts. There are many adorable and very pretty fleece prints as well as juvenile, masculine and feminine prints.