I'm not anything like an expert for monologues, but for musicals, be very careful about doing a song that proclaims how good you are unless you are 100% sure you can back it up. For example, I saw someone audition with "I'm the Greatest Star" from Funny Girl, and the only thought I had was "In your dreams, honey. Next!"
Wicked is a no-no unless you can sing it exactly the way it sounds on the cast album - many of those songs are so well-loved that they're burned in everyone's brain from listening to them over and over - if you can't meet or beat the original, don't try it. I suspect that's the same caveat for Les Miz.
I've said this before, but I recommend avoiding songs from Rent, for 2 reasons. First, much of the "feeling" from Rent songs comes from the orchestration and the emotion generated during the show itself. Singing something like that "cold" and with only piano accompaniment (played by someone who may or may not be able to "rock") will not show you off to your best ability. Second, if you're auditioning for a traditional musical (Guys and Dolls, Music Man, Joseph, Fiddler, etc.) and you audition with a rock-style song, the director may feel you don't have the technical chops to sing more traditional Broadway style music. Hate to say it, but that's my assumption - if I don't hear clear, correct tones, if I hear a lot of swooping and sliding, if I hear a screaming quality in someone's voice, my first reaction is "not good for the long haul - they'll blow their voice out too fast."
Stick with Broadway standards - try to find a similar song from a show by the same composer (for example, something from Brigadoon if you want to play Liza Doolittle or something from Carousel or Oklahoma if you're setting your sights on Maria Von Trapp) - find someone who can play the piano for you and practice with them before the audition so you know how the song will sound without all the lush orchestrations on the cast album.
Oh, and learn the freakin' words. NOTHING makes a director think "Next!" more than someone explaining how they just picked their audition song in the car on the way to the theater, and they don't know the words, so could they look over the piano players shoulder? I've done musicals for more years than I care to count, and have had my share of successes on stage, but I still begin picking out and rehearsing my audition song 3-4 months in advance of an audition. If something comes up at the last minute, I have one stock song that I can always fall back on that shows off my voice, and I use that.
I guess my best advice is being good is better than being clever when it comes to auditioning. Focus on preparation, preparation, preparation - that will take you farther than anything.
Next: VERY EXCITED to be in The Angel City 4, "City of Angels", Buck Creek Players, opening June 7.
"Never try to teach a pig to sing. It wastes your time and it annoys the pig." Robert Heinlein