Low-end mattresses may have vinyl ticking, which can eventually stretch and sag, but most materials should last the life of the mattress. As you pay more for a mattress, the ticking may have a more distinctive pattern. Fancier mattresses have damask ticking with the design woven into the fabric, not printed on it. Some also contain a bit of silk, which is more a marketing gimmick than anything else. In most cases, quilting attaches a few layers of padding to the ticking.
Stitch design varies and is largely an aesthetic consideration.
Top padding is generally polyurethane foam, with or without polyester batting. Batting provides a uniform, soft feel but tends to lose its loft faster than does a soft foam. Middle padding lies below the quilted layer and often starts with foam. Soft, resilient foams feel almost moist to the touch. Foams that feel dry or crunchy won't spring back as readily.