Perforated Business Cards
I love using perforated business cards for games! I also used them to put the memory verse on. One girl told me she had collected all of them and was putting them in the order they would be found in the Bible!
Different suggestions for laminating
As for a laminating machine, business supply or education supply stores will laminate things for you for a nominal cost. Some discount stores (like Wal-Mart) carry laminating film that doesn't require heat. As you said, packaging tape also works.
Blessings,
Julie Burton