Socks - I use Thor-Lo's, which are synthetic fabric. Wool socks are also good.

Underwear - Any wicking, synthetic fabric works well.

Pants - Nylon shorts. Could even use a swimming suit. They dry very fast.

Shirts - Again, synthetics. Or wool, though wool is expensive (and yet, really lightweight wool is good for the summer).

A side-note though is that cotton is not always bad. In the desert it breathes very well, and is a great fabric to use. Of course, you have to always be careful with boiling water when wearing cotton, as it'll bring all that boiling water right to your skin and hold it there if you spill it on yourself. My favorite desert hiking shirt was actually an old 50% cotton, 50% nylon white work shirt... that thing worked great.