Since we don't know who/what "is" Bombadil, we can't really place him anywhere on the timeline. I remember reading somewhere in The Sil that the Ents appeared around the same time as Elves were born, which would make Treebeard one of the oldest (if you count him as a person). Cirdan is definitely the oldest Elf. If we count ainur to be "people", they are older than all the rest, except for Eru.
