Ex-Officio makes men's underwear that are highly thought of on BackpackingLight (got a Highly Recommended rating there). I have women's briefs of the same fabric, and they are wonderful! Well ventilated fabric, no issues at all with chafing or fungus, dry in less than an hour after washing. I like them so much that I wear them for everyday use. Not only that, but the batch I bought over 4 years ago for daily wear are still going strong with absolutely no signs of wear.

I would avoid cotton if at all possible. It's very slow drying and once it gets sweaty and sticky, you will have big problems.
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May your trails be crooked, winding, lonesome, dangerous, leading to the most amazing view--E. Abbey