Clothing to wear in Korea?

I'm going to South Korea in May and I'm a little concerned about the clothing because I know that it is more conservative than America. Honestly it is hard to find conservative clothing in my area. Are short shorts fine? What about sleeveless shirts? Also in America most people don't dress up unless they are going to work. I read that people in Korea dress up all the time. Is this true? I also read that no one wears bathing suits or sungles to the beach there? Any information about the normal attire would be helpful. I want to be as respectful as possible while I am there.