T-shirts can be made by a lot of different fabrics with different composition.
First thing is the raw material which could be either natural like cotton,bamboo,silk etc or can be man made like polyster, rayon etc.
For cotton it's best to take some blend of cotton with few composition of lycra to get the most superior fabric.
5% spandex and 95% cotton is the most ideal fabric for making a roundneck T-shirt and with process like heat setting , biowash, silicon softener washed the ultimate fabric will be the most superior.