My opinion: first, get several of the many available recordings of the "bleeding chunks" - the orchestral excerpts from the operas. Szell, Boult, Stokowski -- many others. Get a few.
Then there are some fun orchestral recordings of the operas without words. Lorin Maazel's The Ring without Words is really good. He also made one of Tannhauser. If you find you like these, then try to locate three RCA cds that Edo de Waart made of Parsifal, Tristan und Isolde, and again the Ring.
If you're hooked on the sound, the luscious harmony, the brilliant orchestral writing then you have to take up the operas. Opera was meant to be seen and I really encourage newbies to get DVDs of the operas - you can turn on the subtitles and it will make a lot more sense. Boy, I wish that was an option when I was learning the opera repertoire. Every Wagner opera is available on DVD/Blu Ray. Read the reviews and look for a close to traditional performance. I am not a snob when it comes to singers. Yes, many of the past were great, and some of the newer aren't as good - but they're good enough for me.
If DVD is not to your liking then you have to do this: get Newman's book The Wagner Operas as a companion to explain and enlighten what you're going to listen to. Then get a good set, like the Warner. Still not exactly cheap, but heck, it's 36 disks. I really enjoy the Philips collection from Bayreuth. DG made a set of complete Wagner operas several years ago that has the three early operas.
However you do it, you might find yourself hopelessly addicted. Then you'll have to go see The Ring live, go to Bayreuth and do all the other Wagner-ite stuff. I love it, but it's so hard to find 5 open hours sometime to listen to Meistersinger or Tristan.
Enjoy!
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