Look into “fishing” shirts. Brands that sell long sleeve breathable shirts will point you in the right direction.

Essentially, they have an equivalent minimum SPF. Usually around 15-20. Brands like HUK and Columbia come to mind but they are expensive and high end. There are many other alternatives.

I'm planning on making my own of white cotton voile or poplin. Poplin might add a tad more sun protection as it's more dense, but anything that actually gets used is better than nothing. I'm not too concerned about SPF rating, because that's only half the point - the right material and construction will also feel less warm than going sleeveless.

Linen is optimal, but pricey and hard to find in good quality, so cotton will do. Woven fabric, not knit, in a light colour will feel the coolest. Ideally something flowy or poofy. Idk your style in clothes, but an oversized button-down will do the trick, and is also fairly easy to find in charity shops. Just check the label to make sure it's pure plant fibre.