Now that we've established that such lists are daft but fun, let's continue. If the first list was purely an intuitive collection of lures, without any didactic or representative pretensions, this list makes more assumptions on the potential listener than just that of a most general, vague interest. I now assume that someone is interesting in 'tackling' classical music; interested in investing effort into the appreciation, fully assuming that any such effort would, eventually, be repaid manifold in enjoyment. The recordings would not necessarily all be equally suitable to a total newcomer because their greatness needs to be unlocked, not just lapped up. This list makes a point of introducing the ear to the more structured forms of sonatas, symphonies, and quartets—including the mono-timbred string quartet as well as choral and vocal works. An opera recording can't be included because of the fiscal restraint; it would have been René Jacobs’ Così fan tutte.
A few notes about recommendations as such: Comments complaining about how any particular selection is purely subjective are redundant, since that's exactly the point of such a list. I try as best I can to divorce personal preferences and general assumptions from my field-tested experiences of bringing neophytes into the fold... but for all the effort, that isn't actually possible. And of course any such static list, however little subjective, still can't acknowledge how everyone's path to classical music is different—radically different even. Ives for him, Bruckner for her, violin sonatas for others, the harpsichord for me. But to deduce from these examples that Bruckner or Ives or harpsichord music would therefore be a good general introduction to classical music is silly, to say the least.
I find that (with few exceptions) the more someone is into classical music, and the more seriously he or she takes it, the less that person is capable of making reasonable suggestions about classical music for beginners. I've heard enthusiasts suggest Bartók Quartets as a good introduction to classical music; either blissfully ignorant of the fact that 99% of general-interest classical music listeners don't even bother with late Beethoven (never mind Bartók), or so blinded by their own feeling of pride and pretension for liking Bartók that they would deem anyone who can't immediately follow them in that field a cretin not worthy of induction into that high-holy temple of classical music enjoyment. In short: the kind of people that would make me adopt Alex Ross' opening sentence from Listen to This — "I hate 'Classical Music': not the thing but the name." The name and all that unsaid haughty pretense that goes with it, including the hypocritical yammering for more popularity followed by derisive sneers if a neophyte sheepishly confesses enjoyment of André Rieu... or the haughty stare when an excited youth applauds after the first movement of a Chopin Piano Concerto. (Because really, they want to continue being an exclusive club of appreciation where liking classical music says something about their social status and refinement.)
Anyway: this second list (shorter, because the recordings I want people to listen to tend to be a little more expensive) after the 'jump':
 T.Tallis, Spem in Alium,Tallis Scholars Gimell     | $17 |
 J.Brahms, R. & C. Schumann , Lieder,W.Güra & C.Berner Harmonia Mundi (oop) | Review on ionarts.
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 J.Haydn 3 String Quartets,Minetti Quartett Hänssler | Review on WETA.
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 J.Haydn, 3 Symphonies,Fricsay / RIAS Orchestra Berlin DG (oop) | Review on WETA.
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 W.G.Mozart, Requiem,Harnoncourt et al. DHM (Sony/RCA) | $12 |
 L.v.Beethoven, The Five Late Piano Sonatas,Pollini DG | "Dip Your Ears" entry.
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 M.Ravel / C.Debussy, String Quartets,Keller Quartet Apex / Warner | $6 |
Total: $100 |