it depends on the size/weight of the quilt as for the hanging to dry- hanging is seldom a good idea (the weight of a wet quilt hanging can pull it way out of shape- or break threads)
it is best to either dry it in a dryer or lay it flat to dry (on nice days i found our hammock great for drying quilts)
when i finish a quilt i throw it in the washer and wash it- i throw it in the dryer and dry it- i care for it exactly the way i believe the recipient is going to care for it- that way i know if it's not going to take it before i give it to someone.