Medium weight, multicolored, heathered woolens that were my dad's. My preference is for multicolored heathers, but they're rare. Heathered socks in one or two tones of the same color are very common. My second favorite socks are linen argyles with a very subtle pattern. Mostly tan with sky blue and light pink. Other than those two, I'm a big fan of Uniqlo and Gold Toe. Here's a picture of some good ones. Sadly, not the linen ones. I can't find them.:
^LtR: wool blend Gold Toe, one of my dad's (I can't find the best pair of those either), wool blend Gold Toe, cotton blend Uniqlo As you can tell, I love heathered socks. Herringbone and other small patters are a close second (well, tied w/ argyles):
^LtR: nylon (I think) vintage, cotton blend Uniqlo I'd love to know a source of medium weight linen or hemp socks. Iammatt recommended Peter Silver, but they seem too thin to me --based only on pictures.