This is one of those occasions where I'd recommend you go over to a specialist sub. If you ask this in MFA's daily question thread, you should get a few decent responses. Honorable mention though to the guy that recommended Asket for basics, that's a great suggestion.

For your aesthetic I'd recommend taking a look around Hinoya Shop. They're a Japanese retailer that carries a lot of the excellent takes on American Ivy, workwear, and militaria that have been coming out of Japan for many years now. Take note of some of the brands you see there and set up alerts on gently.com so you know when items of interest in your size are on the likes of Poshmark, Grailed, Ebay, etc. In addition, check out some of the really great MTO tailors out of Singapore, like Yeossal. Casatlantic is also making great pants inspired by mid-century American and British tailoring at a very good price point (wearing their shorts right now actually). For underwear, I've found Ex Officio's underwear to be a blessing in an east Asian summer.

People suggest Patagucci and Kuhl, but as a guy in South Florida who owns a bunch of both for work, neither brands make anything great for hot weather. They are durable, but you will sweat. That is often the tradeoff. Prana makes lighter pants, but not nearly as durable.