I've almost read every Agatha Christie mystery there is (I've exhausted 3 libraries worth of her audiobooks) and I'm looking to start some of Sayers' mysteries.  Can anyone recommend a good one to start with? I've never read any of her books before.

Not at all, thanks for the tips.  When I like a mystery author I tend to read everything I can get by them.

I was going to recommend one - and realized it was by Josephine Tey :) 

One of my favorite Sayers books, which can be read as a standalone, is Clouds of Witness.  The Wimsey short stories are also very good.

If you are fond of Miss Marple,  I would also suggest Patricia Wentworth's "Miss Silver" mysteries about a retired governesss who works as a private detective. Very good books!

And, of course, Josephine Tey! Margery Allingham is another similar style.

Good recommendations on Sayers' order