Ok, I can give you some recommendations, but obviously I still have alot of musical inexperience, and still so much more music to listen to and be able to add to my recommendations.
If it is to be said that one should get all of Beethoven's symphonies for orchestral music, then the same must be said of obtaining all of Beethoven's string quartets for chamber music. In addition, other string quartet masters were Haydn, the godfather of string quartet music, Mozart, Schubert, Brahms, Shostakovich, just to name a few.
So far, I have all of Beethoven's, Schubert's and Brahms'. Schubert's 9th, 13th "Rosamunde" and 14th "Death and The Maiden" string quartets are my favorites from him. Brahms 1st is excellent, and all of the 16 Beethoven's are terrific, in my opinion. I can't comment on Tchaikovsky, Borodin, Dvorak and other supposedly great creators of string quartets, as I'm not yet familiar with them.
I also won't get into the quintets, sextets, etc., although I do really like Beethoven's Septet, Op. 20, which I don't actually have, but I do have the work transcribed for piano trio.
Beethoven's 10 sonatas for violin and piano, of which # 5 "Spring", # 9 "Kreutzer" and # 10 are must haves.
For some reason, I really really enjoy Piano Trios (piano, violin and cello). There is something about that combination that is very delightful, and it is my 2nd favorite style of chamber music after string quartets. I have all of Beethoven's, Mozart's and Schubert's piano trios. Out of these, the Beethoven # 5 "Ghost", # 7 "Archduke", and # 4 "Gassenhauer" are must haves. For Mozart, I particularly enjoy the K. 502 and K. 254. And Schubert only has 2 complete piano trios, of which the E flat major D. 929 is my favorite.