Hi, I could write at length with suggestions, but I’ll try to limit myself.
Some folks above have suggested some accessible beautiful pieces, such as Pachelbel’s Canon. I’ll add Handel’s concerto grosso Alexander’s Feast, and three discs by pianist Vikingur Olafsson consisting of collections of short pieces by Bach (some transcribed for keyboard), Mozart, and Debussy/Rameau. Outstanding collections.
Bach’s music for solo instruments is varied and wonderful. For keyboard (which I prefer played on piano over harpsichord), there are the Goldberg Variations (many to choose from; I prefer Jeremy Denker’s and Murray Perahia’s versions, along with Sitkovevski’s rendition for string trio), the Well-Tempered Clavicle I and II (again, many to choose from; I like Jennifer Hewitt’s); French Suites (not discussed on this forum much; I like Gavrilov’s); English Suites (Andras Schiff is my favorite). For violin, the Sonatas and Partitas, and I suggest starting with Partita #2 in D, and I like Hilary Hahn although there are many great ones to choose from. Someone above mentioned the Cello Suites (Yo-Yo Ma’s are terrific).
Handel’s concerto grossi are a gateway to his very listenable works; Andras Schiff made a recording of three piano sonatas by Hadyn; and speaking of accessible sonatas, try Uchida’s recordings of Mozart’s sonatas for piano. And, well, speaking of Mozart, his piano concertos, esp. nos. 18-26 (and extra especially no. 21’s second movement (the theme from the movie “Elvira Madigan.”)
Brahms: his Ballades for piano (try Pollini) and for late-night meditation, his Intermezzi (Arkady Volodos).
I’ve gone on way too long and probably suggested too many piano pieces, but here’s one more, which I think is a highpoint of Twentieth Century music, Shostakovich’s 24 Preludes and Fugues, our times’ Goldbergs.
Enjoy!