Hey, Molly!
Here are some ideas for you :)
1) The standard
"I've Got a Crush on You" from Strike Up the Band (Gershwin)
"Easy to Love" from Anything Goes (Porter)
"My Heart Belongs to Daddy" from Leave it to Me (Porter) Also fits in the Comedy Song category!
"Embraceable You" from Girl Crazy (Gershwin)
2) R & H (But I feel like this category is a little limiting... Why not make it Golden Age of Broadway)
"Stepsister's Lament" from Cinderella (R&H) also fit in the Comedy Song Category!
"What's the Use of Wond'rin'?" from Carousel (R&H)
"Many a New Day" from Oklahoma (R&H)
"Johnny One Note" from Babes in Arms (Rogers and Hart)
"Heather on the Hill" from Brigadoon (Lerner and Lowe)
"Life Upon the Wicked Stage" from Show Boat (Jerome Kern) also fits in the Comedy Song Category!
3) Comedy Song
From our previous categories, we already have "Life Upon the Wicked Stage," "Stepsister's Lament," and "My Heart Belongs to Daddy." But none of these songs are modern. So here's a few more ideas:
"Strongest Suit" from Aida
"Mix Tape" from Avenue Q
"It's a Perfect Relationship" from Bells are Ringing
"Schroeder" from You're a Good Man Charlie Brown
4) The Power Ballad - This one is easy! Just use "Suddenly Seymour!" The quintessential power ballad!
Other power ballads that could work for you:
"Almost Paradise" from Footloose
"I Know The Truth" from Aida
"Once Upon a Dream" from Jekyll and Hyde
5) Sondheim
"That'll show Him!" from A Funny Thing Happened on the Way to the Forum (a tad overdone, but an excellent choice for your type!)
"Unworthy of your Love" from Assassins
"I Remember" from Evening Primrose
"Sooner or Later" from Dick Tracy
"Not a Day Goes By" from Merrily We Roll Along
"I Know Things Now" from Into The Woods
"Everybody says Don't" from Anyone Can Whistle
6) Specialty Song
I don't know about this one... do you sing pop, gospel, country, rock, or opera? I personally have found a few pop, gospel, jazz, and country artists that I feel I have a similar vocal timbre and used their songs as audition material. Who's your favorite singer that isn't a Musical Theatre actor/actress? Sometimes it's fun to have songs from male artists too - like Elvis or Johnny Cash, or Queen! Just find something that speaks to you and sounds good in your voice :)
Hope that's helpful!