Over at SFCV, there's a roundup of favorite Ring recordings, curated by Janos Gereben, with contributions by the high and mighty (David Gockley, Martin Bernheimer, David Littlejohn) and the less-than-high-and-mighty, including me. Why on earth this ran in June, a week or so before the opening of Cycle 1, I do not understand. I would have published it in May, so people would have a chance to buy and listen for more than ten minutes..
Understandable space limitations mean contributors can't natter on; instead, they have to make a complex case rather concisely. Herein I get chatty about the Ring recordings I know, because there are tradeoffs of one kind or another with most sets. Surprise - none are perfect, and if you're only going to buy one or two of these sets, you need to figure out what is important to you.
I consider Wagner recordings along several dimensions: the conducting, the singing, the sound quality, orchestral quality, and the completeness. For example, when you're looking at recordings of Tristan und Isolde, a surprising number of the available performances take the "big cut," also called the "Metropolitan cut," in Act II. Thus, to my knowledge, there's no recording of Melchior or Traubel or Leider singing the "Tag und Nacht" section. To hear Flagstad in that music, you have to turn to Furtwangler's 1952 studio recording, which finds her past her prime.
With Ring sets, completeness isn't much of an issue; the studio sets and all of the Bayreuth live sets are complete, as far as I know. The incomplete Ring sets I know of that are worth hearing are Bodanzky's Met Ring of the 1930s - which is heavily cut - and the HMV "Potted" Ring, which was never intended to be complete. Bodanzky was a fiery Wagnerian and worth hearing, despite crazy cuts that, for example, shorten Goetterdaemmerung to three CDs. You need that particular recording because it's the only live Melchior Gotterdaemmerung around.
The "Potted" Ring was recorded between 1927 and 1932, using three conductors, two orchestras, two locations, and a plethora of singers - some of who disappear and reappear in the same act. The sound is good electric-era mono and some of the singing is spectacular. The performers include Frida Leider, Lauritz Melchior, Florence Austral, Walter Widdop, Gota Ljungberg, Friedrich Schorr, and many other good and great singers of the day. I note that John Culshaw spends a page or two disparging this set in Ring Resounding, as part of the reasoning about why he needed to make the Solti Ring. He shouldn't have.
Next, we've got the general issues of sound and orchestral quality. Every set since Solti's is in stereo. Of the great 1950s live Rings, and there are around a half-dozen, only the Keilberth is in stereo. For a first recording, you probably want stereo, to get the full depth of detail and perspective.
Me, I am not so sensitive to sound issues. I listen to the Mapleson cylinders and Julius Block cylinders for fun. Good 50s mono is fine for me, and some of the Bayreuth sets sound great even in mono. Your ears may vary.
The orchestral playing on the available Ring sets varies tremendously. At the top of the scale, you've got the mighty Vienna Philharmonic, the Cleveland Orchestra, the Metropolitan Opera Orchestra, the Dresden Staatskapelle, and sundry other elite orchestras; in the middle, the excellent orchestras on the live Bayreuth sets. At the bottom, there's the unidiomatic playing of the Scala and RAI orchestra and the scrawny Sadler's Wells orchestra of the 1970s. These latter three are paired with excellent casts and tremendous conducting and deserve to be heard.
Ah, yes, the conductors. You will hear a vast range of conductorial approaches to the Ring, from the classic wall-of-sound to the transparent chamber approach; the swift to the weighty to the eccentrically slow. The great conductors all bring something special to their Wagner, and it's worth opening your ears to them all.
The problem boils down to this: if you're only buying one or two Ring recordings, you'll have to figure out your priorities. If you're not counting, then do what I do, and get your hands on every recording that you can. Wagner performances vary more in terms of approach than those of most other composers; the music can accommodate them all.
That said, my personal take follows on some of the sets discussed in the SFCV article. I'll discuss a bunch of sets, and barely discuss the the important sets that I don't own and haven't heard in full, those by Herbert von Karajan, Clemens Krauss, and James Levine.