Trouble is, TR, if you're looking for the "best", it isn't often the sort of thing that is immediately likable to any given individual. For example, I started (like many people) with Romantic music, because that is the classical format with which most people are acquainted, because most film scores to this day are essentially offshoots of the 19th century Romantic tradition. It took me a long time to "get" Bach, but when I did, it absorbed a substantial proportion of my listening.
If I had to propose a list of music's towering masterpieces, it may look like this:
Monteverdi: 1610 Vespers
Bach: B Minor Mass and St. Matthew Passion
Handel: Messiah
the big Mozart Masses
Beethoven: Symphonies 3,5 and 9, Piano Concerto 4 and Missa Solemnis.
To me, these represent high points in the history of music. Monteverdi spanned the gap between Renaissance and Baroque in what was then a very daring fashion. The B Minor is essentially a compendium of all Bach knew about choral composition. St. Matt. is a wonderfully sombre retelling of the Passion story, even if Bach did nick the big tune (from Hassler). Messiah wasn't Handel's first oratorio, but certainly the most loved. The big Mozart masses are wonderful products of a sublime genius. And Beethoven changed the world of music forever and paved the way for the Romantics. As Haydn said on hearing the Eroica, "From this moment, everything is different".
To those I would add as must-haves a Brandenburgs, a Goldbergs, the violin concertos of Brahms and Sibelius, some of Tchaikovsky's ballet music and his Symphony 5. (I'm sure I'll think of more).
However, many folk will not be keen on some of those, because the musical language is not what we're used to. In addition, there are many wonders to be found in the chamber and operatic repertoire, but there are people more versed in those than I. And I really am not keen on most more modern "classical" stuff.