If you wear cycling shorts, they'll either have a pad or a liner, in which case that's your underwear. If you wear something else, such as running shorts, you will probably want some sort of underwear/liner layer, but it'll be your task to find what works. What generally doesn't work is cotton. Cotton gets wet and stays wet, and leads to chafing and other problems (fungal infections, etc.) When I wear single-layer lycra shorts with my recumbent, I'll wear synthetic underwear, usually lycra or coolmax. You can finds stuff that look like compression shorts but are lighter; I find compression shorts still have seams in the wrong places.