08/06/1971 is my favorite show right now. I'm honestly not sure what to recommend if you've never gotten into them because when I first tried, I couldn't either. Then when I listened to them on DOC everything changed, every note and beat permeated into the depths of my being, and I fell in love. So, again, I really don't know, I love literally everything they do now. I think the thing that most people don't realize is how bluesgrass and americana-esque they are, as well as how unpolished they can sound compared to modern bands. If you can get over that though, sweet mary mother of jesus they kill it.
https://archive.org/details/gd71-08-06.aud.bertrando.yerys.129.sbeok.shnf - edit: see if you can find this version on archive or download off bt.etree.org - gd71-08-06.mtx.seamons.96668.sbeok.flac16 It's a matrix of various recordings from the show and is better quality, but from the quick listen I did on what I linked that audience one doesn't sound too bad at all.
Hard to Handle is probably my favorite non-jam song, and this one is the hottest one I've ever heard, as well as one of the longest and jammiest ones as well. Super tight.
St. Stephen is so rock anthem-y, one of the classics for me for sure.
The Other One is sick. And the TOO -> Me and My Uncle -> TOO in this show is SMOKIN'.
And then of course, Morning Dew is an absolutely beautiful ballad with an amazing jam from Jerry.
And as they usually did earlier on, Turn On Your Lovelight as a finisher is just amazing. One of my favorite dead tracks for sure. Sooo much energy and life. Pigpen was truly great.
Also the Mister Charlie here is siiiick. Not their most technically advanced song but goddamn is it a head bobber.
Final edit, the best way to listen to the dead is really to listen to the whole show. That's their whole thing, the continuity, flow, transformation, and improvisation that occurs over a multiple hour time period. Also, watching the new doc Long Strange Trip may give you some context within which to greater appreciate their music and contribution to the world than otherwise.