What a fun question!
Do you have a favorite instrument? Favorite era of classical music? Affinity to a particular composer or conductor or orchestra?
I played trumpet through college, so I'm partial to music with lots of brass. Baroque music often has a lot of high (piccolo) trumpet parts, especially Handel. My favorite classical pieces that have extensive trumpet parts are Mahler's 5th Symphony and Ravel's adaptation (for full orchestra) of Mussorgsky's "Pictures at an Exhibition." Don't overlook Richard Strauss' "Also Sprach Zarathustra" just because it reminds you of an outer space film. Brass ensembles are great fun to listen to: Empire Brass and Canadian Brass are two of my favorites.
My mother and son play cello, so I have gathered quite a collection of cello music. Others have mentioned Johann Sebastian Bach's "Cello Suites." They are extraordinary pieces to listen to, being majestically powerful or hauntingly beautiful through the various movements. In addition to just getting these suites as performed by Yo-Yo Ma (he has several recordings of the Bach suites), it is fascinating to hunt down high-quality pressings by other famous cellists that have also recorded the suites: the seminal album by Pablo Casals, and then Jànos Starker's and Mstislav Rostropovich's pressings are also in my collection, and make for fun comparisons on interpretation.
Another strategy is to find combinations of conductor and orchestra that produced great recordings during the vinyl era; obvious pairings are Leonard Bernstein/New York Philharmonic and Herbert von Karajan/Berlin Philharmonic. Also look for recordings done by great conductor/orchestra pairings that also feature awesome music sections: some of my favorite sources of recordings are the Chicago Symphony under Fritz Reiner and Sir George Solti that also contain the superlative Chicago brass section, with principal trumpet player Adolph "Bud" Herseth, or the San Francisco Symphony during the Pierre Monteux years that had principal trumpet player Charles Bubb, Jr.
I also enjoy vinyl recordings of film scores, jazz, Bossa Nova, French Yé-Yé pop, and bagpipe music, but that will be a topic for another day's question.
Enjoy the listening, and Happy New Year!