Basically badminton clothing simple.
All you need is a shirt and a shorts. (no cup, shoulder pads or shin guards etc, since badminton is non-contact sports)
But, the shirts or shorts need to be comfortable and absorb sweat from the body quickly. The absorbed sweat should be evaporated quickly.
Fig 1: Asics navy/light blue 100% crew neck cotton t-shirt
A 100% cotton t-shirt like the one above is fine for everyday wear, but once sweats starts to build up, it becomes heavy and uncomfortable to wear. Modern sports shirts and jersey are currently made from polyester.
Many badminton companies made shirts from a combination of microfibers, polyester and spandex. Shirts comes in different types, for example a crew/v-neck, a polo-t and a sleeveless shirt.
Fig 2: Li-Ning black v-neck 88% polyester 12% Spandex badminton shirt
Fig 3: Gosen beige 100% Micropolyester polo shirt
Fig 4: Victor black 100% polyester sleeveless shirt
Top it off with a simple shorts
Fig 5: Yonex black 100% polyester shorts
Cotton (natural material) vs Polyester (man-made material)
comfortable under ambient/normal physiological conditions
need to iron
can be eaten by moths
retains sweat longer
Less maintainence, no need to iron
absorb and evaporate sweat away from the body better
maybe a bit uncomfortable under normal conditions (sleeping etc.)