I think the place to start would be from knowing what works by Bach, Vivaldi, and Beethoven you've listened to, and what about them made you want to hear more. If you're interested in exploring classical music in general, you might consider the RCA Living Stereo set, or the Decca Sounds Set, and DGG has something similar as well. Standard rep, decent performances, at a great price for sampling.
However if you're looking for Rachmaninov consider:
The piano concertos with Ashkenazy / Previn
Etudes-Tableaux Hélène Grimaud
Isle of the Dead is one of my favorite pieces I have the recording with Askenazy conducting, but it's the only recording I have of it, so I can't speak for it in particular.
More to the letter of what you asked for here's a list of 10 composers and compositions I like, most with the recording I own. Even excluding opera, my 10 favorites (at the moment) would be off the beaten track. Hell, I"m not sure they've even seen the track.
Sibelius: En Sage & Lemminkainen Legends (definitely the Mikko Frank recording)
Berlioz: Symphony Fantastique I like the Simon Rattle version
Grieg & Schumann piano concertos I'm partial to the Kovacevich reading of them
Debussy: La Mer Dutoit
Rimsky-Korsakov: Scheherazade Reiner or Nolan
Borodin: On the Steppes of Central Asia (really cool where the caravans pass you hear their themes one in a minor and the other in A major play at the same time, then each fades into the distance)
Smetana: Ma Vlast particularly The Moldau Mackerras
Respighi: The Birds, (or the Roman Trilogy) (I have Jansons, Lopez-Corbos, Reiner, but no particular favorite)
Brahms: Symphonies (Haitink) or the Variations on a theme by Hayden
Dvorak: Symphony 9 István Kertész:
BTW classical recordings are much like headphones. It depends on what you want to hear, what you listen for. The "discussion" of the merits of each can easily rival the most energetic thread on this site about any 2 headphones.
