I have a question: what kind of motors are in this vending machine? It's been quite a few years since I've worked on a vending machine, but back when I did 100% of the motors and solenoids ran off of the normal household AC voltage.
The discussion so far has assumed that these are low voltage DC motors. If the motors in this vending machine are line voltage AC, the circuits described so far won't work. In that case, you're probably looking at mechanical or solid state relays.