Saying where to start is tricky. Their studio albums basically just provide the raw material for their live shows and frankly they weren't a very good studio band; also many of their standards never appeared on a studio album. I guess American Beauty or Workikngman's Dead are the typical answers on where to start but they're not any more representative of their sound than any other. Their record-label live albums include Live/Dead (oerrated IMO), Bear's Choice (underratedk IMO; very bluesy with lots of Farfisa organ and shit like that), Skull & Roses (good), and Europe '72 (very good, if really long -- a triple-LP). Come to think of it the early live albums complement the studio albums well in introducing the listener to Dead standards (largely there's not much overlap in material with the studio albums).
TL;DR -- it's probably best to go with a show or two to start because that's their bread-and-butter and getting into them via their official releases is inefficient and can give the wrong idea of the band (but don't overlook their live albums from the '70s).