Outdoor shirt is fairly vague. So I will post a couple. I have a big fan of under armour loose fit short sleeve. My preference it that they seem to fit my body type well which make me more comfortable wearing it when i sweat and it clings. YMMV.

My absolute favorite outdoor hiking or adventuring shirt is a decade old Columbia LS button up shirt. Very similar to Ex Officio or current Columbia shirts. Very light, the sleeves provide mosquito and sun protection but roll up. With a pack on my back I can vent by opening buttons.

A shirt that I like to run with in high temps for long distance is Rail Riders Eco-Mesh Adventure Shirt. Man that thing looks good, breaths great, sun protection. When it gets soaked it dries fast but being super thin it clings skin tight.