Kona cotton would be a good choice - not as paper thin as quilting broadcloth that's commonly sold at places like JoAnn's, but not as stiff as a "bottomweight" cotton twill.
Actually in the pipes:
- Remaking Ser Loras doublet.
- Luke Skywalker, A New Hope
- Wind Waker starter costume in swim material
Eventually: Paul from Dune, Faramir, Harry Sullivan