I'm not sure about shoes for men, but for the ladies, either a leather or suede (leather with soft surface) sole will do. As to anything *above* the sole, get something that is flexible, supportive and will easily form to your feet. Leather will be best (at least, IMHO) here as well.
Good luck with the shoe-quest! 
"Carpe diem, quam minimum credula postero." - Horace