This Warner Classics 6-CD box set was released back in 2004 and features some lovely recordings of late-70s vintage from the much-missed Erato catalogue. This seems to be an absolutely complete survey of Schumann's often ignored chamber music (you might also try the equally interesting Brilliant Classics box
Schumann: Complete Chamber Music), and will be sufficient for all bar those who get the Schumann "bug". Although the recordings are all pre-digital, they all sound very good indeed, so you need have no concerns about the sound quality. Erato was, after all, a premier label in its hayday.
Robert Schumann produced most of these works in 1842, two years after his marriage to Clara Weick. It has been fashionable in the past to deride Schumann's efforts in the chamber music arena, but that's unfair, as much of this music is well-crafted, tuneful, and it repays repeated listening.
CD1 contains two of the best-known Schumann chamber works, the Piano Quartet Op.47, and the Piano Quintet Op.44. The ensemble (Jean Hubeau, Jean Mouillere, Jean-Pierre Sabouret, Claude Naveau, and Jean-Marie Gamard) play these works with enthusiasm and relish; excellent performances, recorded in great sound in 1979. It's always good to have an alternative (non-boxed set) recording of most pieces of music, and I would recommend the ASV Gold CD from The Schubert Ensemble
Schumann: Piano Quintet, Op.44; Piano Quartet, Op.47 as a comparison.
CD2 has two of the later chamber works from Schumann, the Piano Trio 1 Op.63 and Piano Trio 2 Op.80. I rather like these works, despite some of their percieved weaknesses, and Hubeau, Mouillere and Frederic Lodeon (cello) do them proud. For an alternative, more "Germanic" approach, the Altenberg Trio Wein is a good choice
Schumann - Complete Works for Piano Trio.
On CD3, the same ensemble as on CD2 tackle the Piano Trio 3 op.110, the Fantasiestucke for Piano, Violin and Violoncello Op.88 and, minus Lodeon, the Violin Sonata 1 Op.105 with the very short Sonata F.A.E. More enthusiastic and excellent playing will be found here. Schumann's violin sonatas have come back into favour over recent years (quite right, too!) with some excellent new recordings. I highly recommend the complimentary ECM New Series CD released in 2008
Schumann: The Violin Sonatas as probably the best recordings of these moving works.
CD4 contains the Violin Sonata 2 Op.121 and the String Quartet Op.41/1 from Quatour Via Nova in very fetching performances. The other pair of string quartets, OP.41/2 and Op.41/3 are on CD5 with the 5 Stucke in Volkston for Violincello and Piano, Op.112. If you find you like Schumann's hardly-known string quartets, you will want more than these performances, good as though they are. My new reference recording is the Naxos CD from the Fine Arts Quartet
Schumann - String Quartets Nos 1 - 3, an utterly compelling disc, closely followed by the period-instrument Harmonia Mundi CD
Schumann - String Quartets 1-3 by the Eroica Quartet.
CD6 has some "scraps" from Schumann's table in the form of the Adagio and Allegro for Horn and Piano Op.70, Marchenbilder for Viola and Piano Op.113, Three Romanzen for Oboe and Piano Op.94, Marchenerzahlungen for Clarinet, Viola and Piano Op.132 and the Fantasiestucke for Clarinet and Piano Op.73.
This CD boxed set was released by Erato many years ago, and you might find a used copy, but it is unlikely to be as inexpensive as this Warner set
Schumann: Chamber Works. The set comes in a "fat box" jewel case and has brief notes from Raymond McGill that cover the basics.
All-in-all a very good to excellent Warner set, and a very good place to start your exploration of Schumann's never less than interesting chamber music. Recommended.