Don't believe most of what you've read since Robert Altman died. Trying to be helpful, most of the obits compiled a rather obvious list of the highlights of Altman's career. And they pretty much got everything wrong.
Most of the lists I've read suggest starting with 1970's MASH, a possible mention of McCabe And Mrs. Miller from 1971, then Nashville ('75), of course, followed by the implication that he did nothing worthwhile until The Player in '92.
Trust me, if you're assembling an essential Altman collection--and it's going to be a big collection--you can safely skip MASH. Yes, it was the first movie in his long career to be truly "Altman-esque", but it is at best a blueprint for what was to come. Yeah, by all means add McCabe and Nashville to your collection--they're honest-to-God masterpieces--but not at the expense of the work Altman did between them.
Brewster McCloud (1970) and Thieves Like Us (1974) are unfortunately not available on DVD, but Images (1972), The Long Goodbye (1973) and California Split (1974) are. These are essential stuff, especially California Split, the only time Altman ever devoted an entire film to one of his personal demons, compulsive gambling.
And between Nashville and The Player? Again, some of his best stuff. (Just because a movie wasn't financially successful or laden with awards doesn't mean it's no good.) Start with the astonishing Three Women from 1977, continue with the nexy year's A Wedding, 1980's hugely entertaining Popeye, the intense filmed record of Phillip Baker Hall's magnificent stage performance as Nixon in Secret Honor (1984), and conclude with 1990's Vincent And Theo, one of the most moving and despairing portraits of an artist's existence ever created.
Of course, some of these are difficult to watch. Altman's restless camera and multi-layered sound mixes can frustrate those who want every plot point handed to them, but then again, very few of these films depend much on plot. Things happen in them, but often seemingly at random, and you're either on the director's wavelength or you're not. If you are, you'll find that these titles combine, as Altman himself once said, to form one long movie, an ongoing exploration of life, and all the joys and sorrows and frustrations and interruptions we discover on the journey.