Whatever you print them out on had better be waterproof and scratch/scuff resistant, unless you like unhappy customers.
You can do the designs in any of the usual layout programs: Illustrator, Corel Draw, InDesign. Perhaps you can use the other sign software like Flexi, I just don't know those programs. I never recommend Publisher due to my own intense dislike for bad MS behavior.
Something else you can research is being a distributor for Carlson Craft business products, which would give you a wholesale source for foil stamped and thermography business cards as well. There are other business card companies that have similar dealer set-up, like Business Cards Plus (have used them, they are in Michigan), and I believe there is one called Business Cards Tomarrow (never used them).