Well, Foul, since you did some sampling, and I don't think you're the average listener, I suppose skipping Beethoven's Early and Middle quartets won't be a problem. But you should definitely go back to at least the Middle at some point. His piano sonatas are also incredible. I particularly go for the Late, but the famous ones that are often gathered on one disc,
Moonlight,
Pathetique, and
Appasionata, deserve their fame.
Mind you, you could fill a few of those giant players with just Bach, and consider yourself blessed!
Yes, Mozart's
Requiem is great. Actually, one of the very few Mozart pieces that I truly love. His "Haydn" Quartets, so named because that's who Mozart dedicated them to, are also great - particularly the "Dissonance" Quartet. In general, Mozart's string quintets - using a second viola - are considered his greatest accomplishments in chamber music. (But I still prefer the Dissonance Quartet.

)
Regarding Requiems, Verdi's is a cute little piece. You know, the way the Empire State Building is a cute little building.
And, being the chamber music fan that I am, I must recommend Schubert's quintet. Mozart threw in a 2nd viola, but Schubert uses a second cello instead. (It's often called the Cello Quintet.) It is ranked among the top several pieces of chamber music, and rightly so.
Of course, Schubert's greatest genius is for his songs. Not that the quintet is not as good as anything, but he wrote over 600 songs. Not too shabby. In incredible ways, he made the piano an equal part, rather than just accompaniment. And his melodies are achingly beautiful. Be prepared, however, because death and grief are common themes. One teacher said that performances of his brilliant song-cycle
Winterreisse are not joyous occasions. When performed well, there is maybe a smattering of applause, which is for the artistry of the performers. But it's too depressing to give shouts of praise.
Bartok's
Sonata for 2 pianos and percussion is another must-have if his.
Chopin put more emotion and substance into 2-3 minutes of piano music than anybody else ever imagined. Even his etudes are highly musical, whereas anybody else's are nothing more than what the word means - basically, finger exercises. It's easy enough to get complete collections of his Nocturnes, Preludes, Etudes, etc.
I really love Debussy, but he's REALLY different from the others. (Bartok is too, but, uh, different in a different way.) The counterpoint that you and I love so much in the B's is absent. I'm not sure if he'd interest you while you're still so in that groove, but you may as well listen to some samples. You probably know
Claire de lune, which was written for a piano, although it's often heard in orchestral arrangements.
The girl with the flaxen hair is another famous piano work.
Prelude to the afternoon of the fawn is an awesome orchestral piece. He invented Impressionism in music, and most of his stuff is lush and dreamy. (One notable exception is
his piano etudes, which are performed to perfection by Mitsuko Uchida.)