To be honest, it has been a while since I really listened to any Dead stuff, but I'll do my best. With the Dead, live performance is almost ALWAYS >>>>>>>> studio.
As for albums to start with...
American Beauty (just about this whole album is gold)
Workingman's Dead (see above)
Terrapin Station (mainly for Estimated Prophet and the Terrapin suite)
There are plenty of others, of course, but these three are sort of the base essentials, at least as an intro to the band.
Also, everybody knows Jerry Garcia, but the man to listen for in the Dead is Bob Weir. Jerry was always the icon, but Bob Weir is the rock of the band and is certainly, by far, the superior vocalist.
As for live stuff, any of the dozens of volumes of Dick's Picks is good, as is Without a Net (especially if yu want to hear an extraordinarily long but very good 16 minute version of Eyes of the World featuring Branford Marsalis on sax).
And whatever you do, for the love of god, stay far far away from Dark Star. It goes on forever (longest version I've ever seen listed was about 45 minutes o_0....and that's just one song), and it's not very good.