I tend to associate collared t-shirts with school.
I always think of school when i see someone wearing a collared t-shirt.
I always connect collared t-shirts with school.
My first thought when I see a collared tshirt is about school. 聼起來自然嗎?

These are quite natural, with the exception of the last sentence which could also be “When I see a collared t-shirt my first thought is about school.”
A POLO SHIRT is a t-shirt with a collar, a placket and buttons on the placket. Most t-shirts don't have a collar, and are more casual than polos. But it is quite understandable to call them collared t-shirts.