With more than one shipping type scenario like this, it would be better to create a column called ItemType.
you could set the item type value to be "Regular", "FineArt" or "DropShip"
each shipping rule that you create , you would need to reference the ItemType column so that it only applies to the intended item type.
you do this by using the "Number of Items With A Specific Column value" trigger
and the "Based on items with a specific column value" calculation options.