1. Take one of your favorite characters from the actual musical. If you choose a popular character, like Bombalurina, Demeter, or Rumpelteazer, there should be quite a few pictures of your Cat to get ideas from. If you choose one like Tantomile, Coricopat, or Exotica...sorry, there aren't as many.
2. Create a character somewhat like one from the musical. For example, take Bombalurina and make her black instead of red, and red instead of black. Make an "Alonzo" with brown spots instead of black. Give Rumpelteazer purple and pink stripes....anything's possible (with Barbie! Sorry, just HAD to do that).
3. Do a fanfiction or RPG character. Many people make up Cats...I'll bet you do to, whether for RPGs or fanfics. The good thing about those characters is that you can choose whatever you want about how they look--they're your characters, after all. Lots of people do made up cats....and come out with beautiful costumes.
4. Base your costume on a pet cat. I'm sure at least some of you have pet cats at home, and some of them have very interesting markings. It might make for some cool costumes...in the very least, it's fun to draw them as people in CATS costumes and see how they come out.
Chosen your character? Go back to planning!