Unfortunately, your answer for where to start with Grateful Dead is very much going to be based around what era of the band someone prefers.
For example, I love the 80-82 era where their shows were part acoustic part electric. I really like the repertoire and I think, performance wise, this was a peak era. If you are intrigued by this, perhaps Reckoning and Dead Set are a great place to start.
For some people, the late 80's were particularly interesting, and I would be remiss if I didn't sing the praises of Without A Net. The backing interplay of the rhythm instruments and two drummers makes this particularly a poignant listen.
For some people, mid-70's era is paramount. In this case, go big and get the 5xCD box set of the sountrack from the Grateful Dead movie. Rhino put it out a few years ago. Tons of their better known songs from the era, coupled with thoughtful improvisations, particularly the 31-minute version of "Playing In The Band" on disc 1.
Interested in 60's? Try Live/Dead on for size. Documentation of a band in a more primitive time where their voices were still being found, but their search never seems to come off as anything but playful as opposed to assertive.
The answer is that there is no great answer. It takes a LOT of listening over time.
An easier way of answering this question would hinge upon if you prefer instrumental exploration versus concise song performances.