While making your choice, be aware that poly-cotton blend fabrics have their fibers "set" with chemicals that contain formaldehyde (not J. sheets, but all poly-blend cotton fabrics). This slowly off-gasses and can be inhaled, and can also be absorbed directly through the skin, which is like a big sponge. There can be long-term health consequences, especially for children who have contact all their lives.
I've become terribly sensitized to many chemicals, including those in fabrics, many detergents, and most fabric softeners. Many years ago, I actually awakened with chemical burns on my skin when staying in a bed and breakfast. The nice proprietor was very pleased to offer us brand-new sheets. Since then, if I travel, I take my own bedding with M..
Cotton, linen and bamboo are all good choices. It's partly a matter of taste. I have become very fond of stretchy knit cotton sheets. Exquisitely comfortable, and they seem to last a very long time.