Screen mesh, off contact, ink, smoothing station all come to mind to create a thin, smooth print. Fabric can also come into play also.
Vinyl with have even more of a stiff feel than screening. Like everyone said, it mostly depends on the screen ink as well as how the ink sets into the fabric.Thanks for the replies everyone. I would just do vinyl seeing as I'm just starting off and could make the shirts to order. But I'm not sure how good the quality is going to be and how long they will last