Here's a list of some of my favorite random recordings...
Ruthless (Laird), The Grass Harp (Richardson), The It Girl (McKibbins), Thou Shalt Not (Connick), Wings (Lunden), After The Fair (Ward), Little By Little (Ross), Trouble In Tahiti (Bernstein), Coco (Previn), Twelfth Night (Tesori), Applause (Strouse), Sugar (Styne), I Am Anne Frank (Cohen), How Now Dow Jones (E. Bernstein), Wildcat (Coleman), Christine (Fain), Let 'Em Eat Cake (Gershwin), Of Thee I Sing (Gershwin), Balancing Act (Goggin), Dear World (Herman), Fiorello (Bock), New Girl In Town (Merrill), Grind (Grossman), Goldilocks (Anderson), Allegro (Rodgers), Me & Juliet (Rodgers), A Tree Grows In Brooklyn (Schwartz), Desert Song (Romberg), Rags (Strouse), Annie Warbucks (Strouse), Nick & Nora (Strouse), All American (Strouse), Pipe Dream (Rodgers), Purlie (Geld), Centennial Summer (Kern), Very Good Eddie (Kern), High Spirits (Grey/Martin), As Thousands Cheer (Berlin), Late Nite Comic, Leave It To Jane (Kern), The New Moon (Romberg), Tenderloin (Bock), Golden Boy (Strouse), Bajour (Marks), Collette Collage (Schmidt), Weird Romance (Menken)...
Some are more random than others, and some are "cult-y" kind of popular, but after looking through my collection for you, I think I gave you plenty to start with! Some are good, some are awful, and some have only a song or two worthwhile, but all are recordings that most people won't have in their collections.
From the evil she done Lord
Set her free, Set her free, Set me free
Don't let my sorrow
Make evil of me