Rok, that's a very tall order, and a question I had to answer for myself. Forget about boxed sets or anything critics and reviewers have to say.
Billie Holiday had a style so unique and special, that you could hear it in a crowded bar on the jukebox, with drunks making the noises that drunks make, so don't worry about the sound quality; whatever she had when she had it will come through that. Focus on early and mid career, before she began to have health problems. Remember, a person does their best work, and then they become famous; after they become famous, every body is trying to make a buck, consequently every sound they make is the best sound ever, those are the Billy Holiday records I had in my collection that I sold.
Try to audition everything you can and trust your ears is the best advice I can give you, but don't listen to the critics because you might wind up with Billie Holiday records for sale.
Enjoy the music.