I use lycra running shorts, with Coolmax underwear, partly for modesty and partly for wicking sweat. You can use regular padded bike shorts, but the pad acts as a sponge to retain sweat. If you use padded shorts, thinner padding is better. You can use 'street'style shorts, but make sure they don't have seams in the wrong places, and also make sure you can close the legs so they don't act as bee scoops.