Have to admit I like the idea of tagging the races with common, uncommon, rare as it applies to what a DM allows in his or her campaign:
It's a good idea, but I'm not sure I like the terms. They imply a prevalence to those races within the game world, as opposed to options for the DM to choose from in populating the world. It suggests that those "rare" races are "supposed" to be in DnD, just in small quantities, so I'm not sure it quite accomplishes the stated goal.
I think, instead, names that reflect the style of fantasy those races are associated with:
Classic (Human, Elves, Dwarves, Halflings)
Traditional (Half-elves, Half-orcs, Gnomes, High Elves, Drow)
Modern (Dragonborn, Tieflings, Deva, Warforged, Wilden, etc.)