Admittedly, some of Weinberg's catalogue can prove very challenging. This list is targeted at those who might not have listened to his music before, and who might not even be familiar with Soviet music in general.
Weinberg in a nutshell
Weinberg was born in Poland in 1919 into a Jewish family. His father played in a local theatre orchestra and young Mieczysław began helping out, beginning his musical education. He joined the Warsaw Conservatoire to study piano at the age of 14, and narrowly missed an invitation to study in America.
With the outbreak of the Second World War, Nazi Germany invaded Poland. Seeing that life for a young Jew would not be safe, Weinberg fled eastwards, leaving his family behind (they would all perish in the Holocaust). After several weeks exhaustive travel, the 19-year old Weinberg reached the Soviet Union and was accepted as a citizen, with his first name officially changed to 'Moisey'. He studied composition in the Minsk Conservatoire, but had to flee the Nazi advance again in 1941, when Nazi Germany invaded the Soviet Union. Weinberg fled to Tashkent, and his compositions began attracting considerable attention. Weinberg sent the score of his First Symphony to his recently discovered idol, Shostakovich, and the older composer invited him to move to Moscow.
Weinberg was to live in Moscow for the rest of his life, with his music celebrated by such famous performers as David Oistrakh, Mstislav Rostropovich, Kiril Kondrashin and the Borodin Quartet. But he didn't escape the unpleasant side of life under the Soviet Regime. The post-war Soviet political climate became increasingly antisemitic, and Weinberg's father-in-law was murdered on Stalin's orders in 1948. At the height of this political fervour, Weinberg himself was imprisoned for several months in 1953 - it was only after Stalin's death that he was released.
The experience left him a changed man. He dedicated the rest of his life to writing music, much of it in commemoration of the victims of war. Weinberg proved an extremely prolific author, with 26 symphonies, 7 operas, 17 string quartets and many more besides, in a catalogue of over 150 works.
His music is enjoying a revival in the Western World, following a time when he was neglected. This was partly from his own keen sense of modesty, but also because of the huge success of a younger generation of Soviet composers who eclipsed Weinberg. Now, however, his music is beginning to enjoy the success it deserves.
Cello Concerto - Op. 43, 1st movement
Clarinet sonata, Op. 28
Cartoon 'Vinnie Puh', with score by Weinberg
Fantasia for Cello and Orchestra, Op. 52
String Quartet No. 17, Op. 146
Piano Sonata No.3, Op. 31
Piano Quintet, Op. 18, 1st mvt.
I hope that serves as an introduction for you, and you're inspired to listen to more Weinberg. There's certainly a lot more out there. Enjoy!