If you're constantly leaking from the pits, chest, back, or wherever, there are ways to hide this issue. Dark colors like navy and black won't show wet stains that badly, and neither will very light colors like white. Grays, blues, and bright colors are the worst options for hiding sweat, and they'll definitely show the world that you can't stand the heat.
Necessary purchases: J.Crew slim seersucker shirt in navy, $80