If it has to be just one instrument, I agree it would be piano.
Two allowed it would be piano and violin.
Saxophone would almost seem like a good choice, the problem is it can have such a huge variety of sound one can hardly be sure what is the 'definitive' sound. So that rules it out as a great choice for auditioning.
(I have never used a saxophone recording to audition, even though it is one of my favorite instruments!!)
I use stuff with choral, female vocal, orchestral, piano, big/lots of drumming, piano/violin