In 1917, at the age of 14, the child prodigy performed as a soloist with the Warsaw Philharmonic Orchestra. His rendition of Max Bruchs (Brook) Scottish Fantasy won him critical acclaim as yet another Jewish Wunderkind (prodigy). During this period he became interested in the piano, began studying the piano as a composition tool, and started to compose music.

In 1922 he moved to Berlin in order to study violin and composition at the Hochschule fur Music (which was considered the finest music academy in Europe).

He befriended the renowned conductor and composer Paul Kletzky, and together they would visit the home of Zimerik, the owner of the international music score publishing house. His home had previously been frequented by Brahms, Schumann and more. He dedicated his composition Israel Sketches to Pul Kletzky and to the Israel Philharmonic Orchestra, a piece that will be performed by the Israel Philharmonic Orchestra during its 2004 season.(16/11/03 & 04/04) This piece was published by the renowned British publishing house Boosey & Hawkes, and may well be the only Israeli piece published by these publishers at the time.

In 1924 he traveled to Vienna to study with Prof. Hans Gall (Gall notes in his biography that Josef Kaminski was his most brilliant student) and with A. Rozea, who were considered that the very best in their fields. With these teachers, he studied both conducting and composition.

Kaminski returned to Berlin and began to perform as a concert soloist. He was widely acclaimed by the German press.

In 1926, after the death of his mother, Esther Rachel Kaminska, who was dubbed the Mother of Yiddish Theatre, Kaminski returned to Warsaw and was appointed as the conductor of the Jewish Theatre Orchestra, under the administration of his sister, Ida Kaminski. During this period, as his acclaim as a gifted composer grew, he wrote primarily theatrical music for the Jewish Theatre and the Vilna Company, for shows such as Night in the Old Market by I. L. Peretz, and composed songs based on German lyrics.

He founded the Warsaw Quartet (which he managed and lead), a quartet that successfully held numerous performances.

In 1931, Kaminski married Miriam, who was a young opera singer. She stopped performing when they immigrated to Israel.

In 1933, their only son was born. He was to become a pianist.

In 1934, the Warsaw Quartet won the prestigious Pilsudzky Prize as the best ensemble in Poland. After winning the prize, the quartet was accepted into the new Warsaw Radio Orchestra, and Kaminski was awarded the role of head violinist, despite the ranting of the Anti-Semitic press that dubbed them the Zidovski (Polish Jews) Quartet.

During this period as the head violinist of the Warsaw Radio Orchestra, he often performed as a soloist and played the premiere performance of the Violin Sonata by Morris Ravel, who was present during this performance. As a token of his appreciation, Ravel presented him with a signed copy of the Sonatas musical score. He also performed the premiere of the String Quartet by the Polish composer Karol Szymanowsky, who was present at the performance and very pleased with it. In Poland, he befriended Prokovieff and David Ojstrach.

Josef Kaminski was a celebrated soloist, composer and conductor, especially in Poland, Vienna and Berlin. He was the subject of many articles and reviews that praised his musical talents. 

In 1940, Kaminiski composed the Solo and Orchestra Concertino for Trumpet. This work is very unique and is regularly performed throughout the world. The Concertino was dedicated to the trumpet player Konigsberg, and premiered at the Philharmonic, where it was conducted by the composer 1947. In October Shostakovitz wrote that the piece was magnificent, lively, refreshing and perfectly executed.

In 1945, Kaminski composed the String Quartet, and won the Engel Prize.

In 1946, he composed Agmumit (Gloom), dealing with the horror of the Holocaust.

Kaminski was awarded a great honor when he conducted the Philharmonic on a most significant occasion playing the national anthem, Hatikva, in the historic ceremony proclaiming the establishment of the State of Israel, an event held at the Meir Dizengof Museum that was located on Rothchild Boulevard in Tel Aviv. Since the orchestra was set up on the second floor, it was decided that an announcer would notify them at the end of the declaration and they would begin playing Hatikva. The announcer mistakenly climbed the stairs several times, and the orchestra immediately began playing Hatikva, so that the anthem was played several times.