KNIT VERSION: Knit fabrics with at least 20% 4-way stretch are suitable. Cotton jersey, rib knits, lightweight french terry are a few types of fabric that would be great. Generally, sturdier knits are easier to work with and drapier thinner knits are a little more difficult.
WOVEN VERSION: The woven Square Neck top looks great in linen, cotton, rayon, silk, etc! The fabric you choose will affect how your top looks. If you choose a drapey fabric like a rayon or silk you will have more of a blouse-y look. If you choose something like linen it will have a more structured feel.