Euro hinges are not really hinges in the classical sense, they are linkages. So, they are designed to swing the door through a specific path, specific angle, ending up in a specific place. Full overlay hinges are designed for the door to overlap the cabinet side the full thickness of the side, normally 3/4 inch. Half overlay hinges are designed for the door to overlap only half of the side of the cabinet or 3/8 inch. The path the back edge of the door follows as the door swings open is different for the two designs, so a single design won't usually work for both applications. Your stand looks like you need full overlay hinges. But, if the side truly is 1 inch thick the hinge may let the door hit the outside edge of the side, especially if the door opens more than 90 degrees. The hinges come with mounting plates, so no you don't need to buy them separately.