OP here. Lots of great ideas, everyone. One I will throw into the mix is a ghost linage/template. I have no idea how it would work, but it would be cool.
The way this discussion is going I see picking your race as being two choices.
1) Pick your linage - human, elf, dwarf etc.
2) Pick your template - unchanged (you are your linage), anthropomorphic (animal person), awakened (tree, dog etc.), undead etc.
If rules could be figured out a linage or template for Aberration, Beast, Celestial, Construct, Dragon, Elemental, Fey, Fiend, Giant, Humanoid, Monstrosity, Ooze, Plant, Undead would be cool. Then you could play every type of creature.