first: some history
It turns out that there was already as detailed a history of this group as any, hiding in plain sight in the liner notes to the Grisman's wonderful collection DGQ20: A Twenty-Year Retrospective 1976-1996 by Pamela Abramson. I will take the liberty of quoting it in full here, with some additional notes.
The acoustic revolution that coincided with the advent of the David Grisman Quintet in 1976 wasn't planned, nor was it accidental. New ideas had been brewing in the heads of creative bluegrass and folk musicians throughout the late 50's and early 60's, extensions of those original radical folk musical concepts of Bill Monroe and Earl Scruggs, who were certainly radical when they altered the face of old-time string band music in America. Blues and jazz had influenced bluegrass musicians, as European classical traditions had influenced black music, but the time was ripe for even more ingredients to be tossed into the melting pot of contemporary American roots music. So there’s the official name for posterity, I suppose. I opted for Great American String Band in the prior post, since that was how they were billed for the June ’74 shows. Notice there's no mention here of David Nichtern at all, which I infer to mean that his involvement wasn't central to the group’s concept… but I wonder what he would say about it. By November 1974, at any rate, he was leading his own band: http://www.concertvault.com/david-nichtern/record-plant-november-09-1974.html
In 1974 mandolinist David Grisman and violinist Richard Greene, with Jerry Garcia, Taj Mahal and others, formed a loose aggregation called the Great American Music Band.  The concept was simple: sophisticated folk and bluegrass instrumentalists creating a format to play and improvise without vocals. The repertoire would draw on varied sources: traditional fiddle tunes, swing tunes from the Hot Club of France, and music from great American composers Bill Monroe, Fats Waller, and Duke Ellington. David Grisman had also been writing music, mostly bluegrass style mandolin tunes, patterned after those of his heroes Monroe, Frank Wakefield and others. Now, with this new vehicle, David started composing pieces with greater scope and a more personal stamp; "dawg" music had come into being. By the end of the year, Grisman and Greene had settled in with their own band which included guitarists John Carlini and Ellen Kearney , with bassist Joe Carroll. The group generated excitement opening shows for many headliners, from Bill Monroe and Maria Muldaur to the Grateful Dead. By the spring of 1975 Greene had left the band to work as a sideman for Loggins and Messina.  Dawg remained with a bunch of newly-composed tunes, a bass player and -- most importantly -- a concept. Soon David's mandolin protege Todd Phillips was jamming with his teacher and Joe Carroll on Dawg's back porch. One day Todd brought a friend, fledging fiddler Darol Anger, who soon became a regular dawgmaniac as well. With Carlini touring with the Ice Capades, and Kearney off somewhere else, the new ensemble rehearsed without a guitarist.
In the spring of 1975, Tony Rice was leading his own flatpicking revolution as guitarist with J.D. Crowe's New South, arguably the finest bluegrass band of its time. Tony met Dawg early one morning in Washington, D.C. after they had both arrived to play on banjoist Bill Keith's first solo recording project. Rice was curious about the music of the Great American Music Band and, upon hearing a tape, expressed great interest in playing this new music. By October, he had decided to leave Kentucky, move to California and play guitar at David's down-home rehearsals.  He also named the band the David Grisman Quintet. With more tunes coming all the time, two mandolins, bass, fiddle and the world's greatest flatpicker, the DGQ was born. 
 Ellen Kearney, interestingly, has been noted as sitting in with the Garcia/Saunders band at the Bottom Line in July 1974, joining Maria Muldaur on vocals. I can only hear Muldaur’s vocals on the circulating recordings, but that doesn't mean Kearney wasn't there. She recorded and performed for a few years with Muldaur, including on her hit debut album (also with Nichtern, Grisman, Greene, etc), then seems to have dropped off the professional music scene a few years later and left California to focus on family. Here's an article that fills in some biographical details about her: what little I've found about her seems to downplay her guitar playing, but she must have had some serious chops!
Also, a thread at the mandolincafe forum has some interesting responses that fill in some more specifics about the early days of the GAMB/DGQ. I see some mention of tapes of the 1975-era GAMB, so this stuff is out there somewhere.
 Corry has a history of Richard Greene's early career here:
As busy as he may have been, he did continue to work with Grisman; he toured along with the DGQ in Japan in 1976, for example: http://db.etree.org/lookup_show.php?shows_key=422510
 So here’s a fascinating moment of synchronicity, found on the the complete Pizza Tapes (Extra Large Edition) release, in the first track:
Grisman: It’s a trip seeing you guys together.
Tony Rice: Should have happened a long time ago.
Grisman: Well, the funny thing, y’know, I was telling Jerry before, the day I came to get you at the airport, the first time you came out here, I guess the first time we got together out here, I ran into Jerry earlier that day and we were jamming at my house and then—
Rice: —then you had to pick me up at the airport—
Grisman: —and then I had to pick you up, and that’s the last I played with Jerry for a bit, 17 years.Um, wow. Even if that’s not 100% accurate, it does indicate that Garcia and Grisman remained casually connected until well into 1975, around one year after Garcia left the GASB. Dunno how that fits/contradicts any other narratives about their partnership, but there ya go.
 a later note in DGQ20 also indicates that the band rehearsed for four months prior to their Jan 31, 1976 debut performance.
Also, "fledging fiddler Darol Anger" is my new favorite tongue twister.
second: some tunes
I really like how those notes lay out Grisman’s musical vision very clearly while locating it within a broader 20th century tradition of blending different folk genres with more "sophisticated" or "cultured" traditions. So, in that spirit, here are some specifics about the band’s repertoire circa mid-1974, broken down by genre. I assume that they didn't have too many other tunes under their belt, since the setlists are fairly repetitive and they were playing Swing '42 twice each night.
traditional/old-time fiddle tunes:
- Colored Aristocracy - info
- Methodist Preacher (Bill Monroe/trad) -- played mostly as a fiddle/mandolin duet; info
- Billy in the Lowgrounds (trad/Irish) -- played mostly as a fiddle/banjo duet. OAITW also played this. Note that Greene introduces Garcia as "Earl Spud," probably joking on Earl Scruggs' name (Scruggs did record this song).
- Lonesome Moonlight Waltz (Bill Monroe) -- a classic bluegrass instrumental, which the DGQ continued to perform.
- Maiden's Prayer (aka "Virgin's Lament") (Bob Wills/trad) -- this was also recorded by Buck Owens' Buckaroos featuring the great Don Rich, a major Garcia influence.
- Bud's Bounce (Bud Isaacs) [thanks to anon commenter for the correction!] -- a popular country pedal steel instrumental. It's a pity Garcia didn't break out the old Zane Beck!
- Drink Up and Go Home (trad/Feddie Hart) -- deaddisc. An outlier vocal tune; Garcia sang this in his pre-GD days, once with the acoustic GD in 1970, and with Garcia/Grisman.
David Grisman "dawg music" originals:
- Cedar Hill (Grisman) -- DGQ20 notes this was Grisman's first mandolin composition, written in 1963, and was performed at the first DGQ concert in Jan 1976. OAITW performed this, as have other groups: deaddisc.
- Dawg's Bull (Grisman) -- deaddisc
- Dawg's Rag (Grisman) -- deaddisc
David Nichtern originals:
- I'll Be a Gambler If You Deal the Cards (Nichtern) -- vocal
- My Plastic Banana Is Not Stupid (Nichtern) -- instrumental
Django Reinhardt and 20's-30's jazz standards:
There's only one actual Reinhardt original here, but most of these were recorded by the Hot Club and are associated by many with Django:
- Swing '42 (Reinhardt)
- Limehouse Blues (Braham/Furber) -- a 1920's showtune that went on to be a standard with many, many jazz musicians, including Django. info
- Sheik of Araby (Snyder/Smith/Wheeler) -- info
- Sweet Georgia Brown (Bernie/Pinkard) -- info
- Russian Lullaby (Irving Berlin) -- via Argentinian guitarist Oscar Alemán, an old favorite of Garcia's. Grisman's Acoustic Disc label released a collection of Alemán's recordings, which I believe is the only American issue of his work? Multiple jazz musicians have played it since; notably, John Coltrane recorded it on Soultrane (1958), a record that Garcia admired. I don't believe Django ever recorded this.