A coin mechanism is just like any other input in the system, such as buttons or joysticks. It is just a microswitch or two, but rather than activating it with a lever or a button, a coin trips it after it is validated in the mechanism. So yes, you just hook them to the coin inputs on the iPac, or to whatever inputs you want to use if you want to change the settings.
Most coin mechanisms are standardized so that they will fit other coin doors, such as the mechanisms used with standard over/under coin doors. The mechanisms from Ultimarc are a proprietary thing that don't work like a standard coin mechanism at all. The ones that Arcadenerd sells are standard coin mechanisms I would assume, which would fit a standard over/under coin door.
The coin box or bucket is just a receptacle for the coins. You can use a tin can if you want—they aren't essential for the mechanism to function.