An A-shirt is essentially underwear. And in that capacity, you want something that is comfortable, feels nice on your skin and breaths.
Cotton with a hint of something stretchy, maybe rayon, or a fine knit. I suggest you go to the fabric store and feel around a bit.
While stretch is not required, it does make sense for underwear. That being said, you can make this in a non-stretch, just make sure pick loose or casual fit.