One of the popular styles has heat shaped cups, but to retain the shape it has to contain some polyester. Using a fairly breathable fiber in conjunction with cotton can give the softness of cotton and not lose the needed support. Take notice where the lace is. Lace is pretty, but it can be irritating if placed in a position where it rubs your skin. The majority of strap styles have a hook opening at the top with three loops for expansion.
Some styles come with a center snap.
Most of these styles are made with a knit - so the expandability comes from the stretchiness of the knit fabric. Other styles have center front hooks, a variety of patented plastic snap closures or no hardware at all. These are designed to pull down or up to nurse. They can be very comfortable and work well but make sure there is no tightness across the top of the breast that could prevent drainage and clog a duct - this goes for pulling the cup down under the breast as well. The style of opening is secondary to the fit.