Nina Simone

Nina Simone's start is interesting:  she began playing piano in church, aspired to be a classical pianist and studied at Juilliard, but in order to pay her way through school she began playing clubs and started to sing jazz standards.  Though she's playing jazz in her early work, you can definitely hear the classical and gospel influence.  Her version of "I Loves You, Porgy" is heart-breaking and fantastic:

Here's one of her later performances: