Mary Stallings, Rene Marie, and Laverne Butler are excellent JAZZ singers. Each very different but they are not warmed up pop singers! :-) You should try them if you can. BTW, Etta Jones is great.
If you haven't got it there is a recent compilation disc on HighNote "Always In Our Hearts", "Etta Jones as we loved her". For anyone starting out this is as good a place as any.
And, if you want a real jazz singer who accompanies herself, and you appreciate something a bit laid back, I endorse previous recommendations for Shirley Horn.
And, lastly, I'm also going to endorse recommendations for Eva Cassidy - she really hits a chord for me and reaches into my heart with several of her renditions of popular songs. I save her music for special occasions!
Enjoy.............