T-shaped backsI'm talking about backings that have two pieces of fabric running in one direction and another running perpendicular. Thusly:
I can tell you that longarmers hate T-shaped backs. This is because of the warp and weft (or crosswise vs. lengthwise grain of the fabric). There is a little bit of stretch in the weft (crosswise, that is, selvedge to selvedge) grain of the fabric. When a longarmer is loading a quilt onto the frame, she has to work against gravity. That gravity is pulling down on the backing, which isn't actually attached to anything but a couple of roller bars on her frame. This means that the backing may sag and if it's sewn together in a T shape as illustrated above, it will sag weirdly. So, if you're sending your quilt to a longarmer, skip the t-shaped backing. In fact, if I were sending mine off, I would piece the back as little as possible.
Wide backings are a popular choice, but keep in mind that they are often not made from the same high quality greige goods your regular quilt shop fabric is made from. So, wide backings can also be hard to square and they can be squirrely.
I also understand that longarmers aren't fans of using bedsheets as backings. this is because the thread count on sheets is often too high to easily quilt through.
This is the super soft, furry stuff that is so wonderful to touch. Longarmers don't seem to mind minky fabric on the back of quilts. Remember that quilting stitches will really disappear into your quilt if you use minky fabric on the back, so if you're wanting to highlight the quilting on the back, minky might not be your best choice.
Quilting at home
So all of the things above that I mentioned that longarmers aren't fans of? Well, they're often more do-able at home. If you're basting your quilt on a table or the floor, you don't have gravity working against you. And though I haven't used a sheet as a back before, once I scored a used duvet cover from Crate and Barrel for under ten bucks and used that as a backing and it was just fine. But, it wasn't really a sheet, and because it was Crate and Barrel, it was of reasonably high quality.
A note about using minky: please don't use the yucky stuff they have at the discount fabric stores. That stuff feel okay (not as good as quilt shop Cuddle) but once you wash it, yuck. And contrary to popular belief, it isn't too bad to quilt with, as long as you use basting spray and not pins to baste.