Some essentials - "Pure Ella" from Ella Fitzgerald. On this one she's accompanied only by piano (a masterful Ellis Larkins), which puts the spotlot more firmly on her than most recordings. And she's at a peak.
Billie Holiday -- the Columbia sets, "The Quintessential Billie Holiday" are uniformly good to great. I'd say start with Vol. 4 or 5 (or 3). These are all single-discs. Or if you find "Billie Holiday Sings". I don't know whether to steer you toward or away from Lady in Satin. It is the sound of a woman breaking. Some people adore it, and I do sometimes, but always feel a bit morbid admitting it. I'd say only for the committed, so don't start there (even though you'll see it every time you look for Billie).
Betty Carter - The Audience With Betty Carter. This is improvisatory jazz of the highest order. It's a double CD.
Sarah Vaughan - Sarah Vaughan with Clifford Brown (on EmArcy, or Polygram). Her records are rarely this good, in spite of her having one of the most amazing instruments of any singer ever. Here you have a great record, with her voice also at an absolute peak even for her (and with the great Brownie on trumpet, it's not fair how many ways this recording can rip you to pieces when it feels like it!)
I'll plug another personal favorite, Sheila Jordan's "Lost and Found". Already not a youngster by any means on this one, and she still sounds amazing, utterly unique on a set of standards. Right there with the other royalty.
