>>18462394in order that's dobby cloth, gauze, poplin, voile, hopsack, chambray (note: usually looks more like denim and usually isn't so airy, that's an unusual chambray)
and the pic in this post is seersucker (my favorite)
you can probably find most of those in cotton or linen or a cotton/linen blend pretty easily.
there's other good stuff out there (silk, tropical wool, tons of other less common cotton weaves) a good way to discover them is browsing the uber high end brands s/s collections and seeing what they make their shirts from. sadly i've never really found a single article on summer textile that doesn't miss a ton of weaves.
linen's fine btw. i was just making a point that cotton or wool can be woven even thinner/more airy and that the weave matters even more than the fiber its made of. its also worth knowing that linen's one of the few fabrics where a blend can be preferable to 100%.