Of the female jazz vocalists you have mentioned, I would recomend the following recordings:
Since you find Lady Day's voice during her Verve years too raspy, I would recommend her Columbia recordings. These came in two great LP sets: Billie Holiday "The Golden Years" Vols. I and II. Another great recording from her 1944-50 period is The Billie Holiday Story, originally released on Decca, re-released on MCA. On these three sets you will hear the songs that have become identified with her when Billie was in her prime.
Ella never sounded so relaxed and unselfconscious as when she recorded with Armstrong. All of the recordings they made for Norman Granz's Verve in '56 and '57 are absolutely wonderful. Granz also produced a fine recording of Ella and the Duke Ellington Orchestra in '56 and '57 called Ella Fitzgerald Sings the Duke Ellington Songbook Vol. I, with strong accompaniment from Hodges, Kessel, Webster, Nance, Anderson and the rest of the Orchestra. You will also want to hear Ella's classic If Dreams Come True that she recorded with Chic Webb in '37 and Ella Sings Gershwin, recorded on Decca DL74451.
Sarah Vaughan made several memorable recordings. Let me suggest two: Sarah Vaughan, recorded on EmArcy in '55 with Clifford Brown and others; and, How Long Has This Been Going On? w/Peterson, Pass, Brown and Bellson recorded in '78 for Granz's Pablo.
Betty Carter's recording on Bet-Car entitled Betty Carter is deserving of its spot on Lyons' best 100 jazz recordings.
I agree with Kana that Ernestine Anderson's Live From Concord to London is one of her best recordings. But I prefer Never Make Your Move Too Soon on Concord, 1981. It's got it all: Anderson in top form, tasteful selections, great accompaniment from Alexander, Brown and Gant, original arrangements that swing.