Two of the previous posts hit the nail on the head. Depending on my MtoF crossplay, I wear very short , yet very puffy bloomers, usually with ruffle trim at the elastic around the legs. These hide everything and are very comfortable, yet coordinates nicely with my costume (or my sweet lolita dresses). For my Sailor Moon type costumes (short pleated skirts) I wear spandex "cheer" briefs. These are very stretchy and cover everything and look "correct" in case anyone gets a glimpse up there!
I ALWAYS stay away from thongs. I know many crossplayers who try to wear them and it looks quite scary. They only are good for wearing under very skin tight pants. I also never wear male underwear or "boycut" female underwear. After all, I AM crossplaying. I dont want to wear anything "male" when Im crossplaying!