I wear lycra, but touring, I second the motion for LIGHTLY padded undershorts like Andiamos. They dry very quickly, they're cool and comfortable. I wear light pants-shorts-knickers over, high on synthetic content. That way, I can arrive, strip the undershorts and wash them, and put the top layer pants or shorts on and I'm good to go.

Three tips: the right saddle, broken in (I'm a Brooks guy), scrupulous cleanliness, and a proper pair of shorts. One of the advantages of the two layer system is familiar to any old school hikers who wear two pairs of socks. Nearly all the rubbing happens between layers of fabric, and not between fabric and your nether regions.