So I've been listening to that Adventure Zone D&D podcast and it's fantastic. Speaking as someone who has no experience with D&D, it's amazing how much more enjoyable a game of D&D is with a good DM, and Griffin McElroy is a DAMN good one. Absolutely hilarious. I especially love all the voices he does for the different characters. Thanks to the people that recommended it to me a few days ago.
"He sounds like Kelsey Grammar, and he looks like Common. He is one hell of a goblin."
You're absolutely right about the DM being key. Being able to take the players' ideas and immediately go along with it is so important to maintaining the flow. Strips out all of the rules-heavy baggage of the game, hides it behind the DM's screen and leaves the players to get on with Doing Cool Shit. The players don't need to know the rules even, they just explain what they want to do and a good DM will, improvising as necessary and without skipping a beat, tell them what to roll.
Once you're done with TAZ (or rather, caught up and are left with the rest of us, waiting for the latest episode) you might want to try
the Acquisitions Incorporated series; it's Mike and Jerry from Penny Arcade with Scott Kurtz from PVP as players (Mike's never played), being DMed by Chris Perkins, the once lead designer on D&D. Suffice to say, the guy's a good DM who knows his shit. There's a brief session early on where another DM steps in and it's fascinating to see how this other guy's differing DM style clashes with the group. Where Perkins is a "I want you all to have fun" DM, the brief stand-in is a "I want to make you guys bleed" DM.
The audio quality of the podcast starts off rough, being just a phone on the table, with little if any editing. I don't think any of the crew involved expected it to run for eight seasons or feature as a prominent main stage PAX event. I think it was initially just a single one-off promo podcast for D&D 4th Edition. Comedy-wise, it never reaches the heights of TAZ, and I'm not sure anything will, the McElroys' chemistry and comedic improv talent is too strong, but the Acquisitions stuff certainly has plenty of funny moments. The live shows from PAX are a unique spectacle for sure.