The Amethyst applies a Set Affix (the green affix) to the item. An item can only have one Set Affix.
You can find what Set Affixes cannot be obtained through Amethyst here:
The affixes you will want most for farming are:
Gold Find, Item Drop, Luck, Pickup Radius, Fortune, Crystalline, Eternalized, Mythical, Nadroji, and All Sets +2. Some other affixes that work well with farming affixes can be added add well: Faun's Gifts, Satyr's Spirit, etc.
Oh, and a Hunter Ring.