Lifelong Deadhead here. I too started with the more accessible studio stuff and steadily disappeared down the wormhole of their live performances
First thing to understand is that Grateful Dead of the studio albums is a very different beast to the Grateful Dead of the live albums. Both are wonderful, but in different ways. They are almost unique in that they recorded and archived almost every single concert they ever played onto high quality multitrack and then made them available to fans. Originally they released them to fans via unofficial tapes which got passed about and copied (with the band's consent). But then due to demand they released two official series of CDs: Dick's Picks (36 volumes !) and Dave's Picks (54 volumes !) named after their archivists. So there's literally hundreds of concerts available spanning their entire career and they are all top stereo quality, not bootleg quality. All very daunting for the newcomer.
Here's where I would start: there's a bunch of studio albums that have a lot of their more accessible songs that made it into their live sets: American Beauty, Workingman's Dead, Blues For Allah and my personal favourite Wake Of The Flood (which is where I started). There's also several very good live albums in their regular releases: Europe '72, Live Dead and the live acoustic Reckoning. But good as these live albums are (especially Reckoning IMO) they aren't a match for what's on the live Dick's Picks and Dave's Picks archives.
So if you like what you hear I would then start dipping into the Dave's Picks and Dick's Picks archives (they're all on Amazon Music and other streaming services). Everyone has their personal favourites, I prefer the concerts from 1973, 1974, 1977 and 1980. If you get this far I can recommend a few of the best ones (IMO).
Then if you can't get enough there's Dead And Company which was formed after Jerry Garcia's death by Bob Weir and several of the other surviving members, plus some great new musicians, including Oteil Burbridge on bass and ... very surprisingly .... John Mayer replacing Garcia. I was very sceptical at first, but they really capture the Deadhead spirit and hearing this side of John Mayer's playing was an eye opener. There's a whole long series of their concerts available too. But don't go there just yet, not until you've listened to the real thing
Wishing you a "long strange trip"