I personally am debating whether to get this navy pique fabric in a popover. The description makes it sound almost knitted in how it moves, so I’d make it a cutaway collar to make it a quasi-polo that I could wear under a navy sportcoat with white pants (one of my favorite, go-to looks).
My go-to fabric year-round, though specifically in the warmer months, is cotton-linen, and they have an excellent selection. I love this framed stripe, and this solid blue Oxford-weave cotton-linen best.
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I also quite like their $85 Oxford cloths. Their Ivy Button-down collar is one of the best contemporary button-down collars out there. With the shipping/handling fee waived, $85 for a custom-fit shirt is tough to beat.
And if you haven’t ordered from Proper Cloth, use this link to get $20 off your first order (which also gives me a kick back, too).