Some lines of fabric are just a lot stiffer than others. Stiff fabric, starch and less than drapey batting combined, and you have a problem!
I use warm and natural, and don't usually have an issue with stiffness, but my quilts get hung up on the front edge of the Sew Steady quilting table topper I have. One way I have found to remedy that is to put a satiny pillow in my lap. It helps the quilt glide around and not get hung up. (Actually, I don't have a satiny pillow: I put a regular pillow inside my nylon windbreaker and zip it all up.)
I think many people would advise against sewing all around the edges first. I have had pretty good luck in starting at one edge, about middle way, and working towards one side, all the way to the side, then work on the other side. It seems to me that if you sew around the borders first, you have sort of fenced yourself in. If there are any puckers, there is no way for them to be worked to the side and out. Puckers can be created where there was none before if the walking foot tension is a little strong, or if one of the fabrics is a little stretchier than the other, as in working with a flannel backing.
Probably someone else will be able to give you ideas of other types of batting to use. I live in a fabric desert here now that Hancock's closed up, so my choices are limited. Warm and natural is available at Hobby Lobby, so that's what I use.