I don't know Widespread Panic, will have to check them out. I've listened to a few Phish albums. I think my favorite track (heard thus far) is
...although always open to recommendations.
Very interesting you were drawn to that Phish track, Toby. It has sort of a dual reputation of being a favorite of new fans (or did when I was more into the Phish scene years ago) and also being a good launching pad for extended jams during a certain era of the band. The song itself has never been one of my favorites, but some of the best bits of improv have come from it, so I'm appreciative.
If I were making recommendations I could go on for a long time, but for a few very different, but very good intros, check out:
Tweezer. Because this version was on an officially released live album, A Live One, it was a lot of people's first introduction to Phish's "type II" jams (i.e., improvisation that breaks entirely from the underlying track instead of vamping on the basic melody of the song). Some might want to look for something a bit more obscure (and there are plenty of other great versions of Tweezer out there), but there's a reason it was chosen for A Live One imo.
What's the Use, an extended instrumental track with a little more darkness and grit. This version is a soundcheck from the Fuji Rock Festival in Japan in 1999.
Simple. A much spacier vibe and another officially released track, but I was at this show when it was recorded and remember thinking that this was probably the best version of Simple of all time. And it is.
You Enjoy Myself. The absolute classic Phish song. I love love love the early, tight, composed tracks, which they pretty much stopped writing in the mid 90s (or at least stopped writing those that demanded as much proficiency to play as the early ones). But this is one of the better versions of a song they've played hundred and hundreds of times.
Finally, just put on this full live album, Slip, Stitch and Pass. You'll love that it starts with a cover of Talking Heads' Cities and it gets better and better from there, particularly the second track, Wolfman's Brother.