None of the dates are rare. What I have noticed here at CCF that one date, material, size, MM (or not) combination is harder to find in various regions. For instance, the 1982 D LD Zinc is harder to find here in Connecticut. All the others are relatively common. But in places (e.g. mid-west), that variety is rather common, but other varieties for the date are not.
Location, location, location.
As for sorting copper cents from zinc, a postage scale is a quick way to sort/confirm material. Some use the 'drop' test, listening for a thud (zinc) or a ring (copper). And after sorting thousands of them, you get to a point that you can spot one or the other visually with a very high success rate.
Good luck on the hunt!