You might want to add ALW to that "no" list.
Whatever song you choose, make sure it is relatively easy to sight read. The 32 bar rule is also good and make sure there is a good 16 bar part that you can pull out of it. A good audition song ought to last you for years and not just for one audition.
Look at My Fair Lady and Camelot since Julie Andrews sang the lead in both. I Could Have Danced All Night is a great song, but to put a contextual spin on it, try to convey that you are NOT singing about dancing. You get my drift?
For ballads (and to own a cd of a great unappreciated score) listen to House of Flowers. A Sleepin' Bee is a classic.
"If my life weren't funny, it would just be true. And that would be unacceptable."
--Carrie Fisher