From my mining experiences of trying to obtain all the fossils I'm sure that the rarest items are definitely the fossils. It seems to my perspective anyway, that the percentage of fossils spawning are really damn low, however I'm not sure if there's a percentage applied to the TYPE of fossil that will spawn (IE Helix, Claw, Root, etc). However, I had never mined a rock that had 2 fossils at once.
Plates are just as rare as the fossils or a little less rare. Going up the list is the evolution stones (not counting oval stone cuz that's pretty common), and then Max Revives -> Heart Scales -> $$$ items like rare bones, star pieces, etc. -> Odd keystones (surprisingly common) -> hold items and shards being the most common.