Occasionally I've had immensely rare records though my hands. Recent examples are SAX 2531, Leonid Kogan & and Elisabeth Gilels playing Sonatas for Two Violins, and SAX 2386, Kogan again, playing the Beethoven Violin Concerto with Silvestri conducting. I think one of the reasons why an LP is rare, is that the reviewers at the time were not enthusiastic about it, so not many people bought it. This certainly seems to be the case with SAX 2386. The Stereo Record Guide volume 3 only gives it one star and another in brackets, and much prefers Menuhin's recording, again with Silvestri conducting, on ASD 377, giving it 3 unqualified stars. So ASD 377 sold hundreds of copies, is nowadays quite easy to find, so doesn't command a high price on the collectors' market. Indeed modern collectors are much more interested in Kogan than Menuhin. I'm interested to see that another prized SAX, Oistrakh playing the Beethoven Violin Concerto on SAX 2315, with Cluytens conducting, only gets 2 stars and a third in brackets. The Stereo Record Guide says "For some odd reason Oistrakh is not up to his usual form". Which may explain why original silver/blue label SAX 2315 commands a higher price on the collectors market than original white/gold ASD 377. It sold less well at the time. Of course original SAXs are now one of the most prized of the early stereo labels.
SAX 2531 is a different matter, I think. The Sonatas for Two Violins are by Leclair, Telemann, & Ysaye. Leclair & Telemann are of course both Baroque composers. In 1964 there wasn't a lot of interest in Baroque Music. Vivaldi wasn't the household name that he became later in the 20th Century. So I suspect there was a very limited market for this recording. I also wonder if the Cold War in the 1950s and 1960s coloured customers' and reviewers' views of Russian performers. But that is pure speculation.
Two of the violinists of the 1950s Johanna Martzy and Gioconda de Vito, made records that are now pretty rare. Again we probably have the critics to thank (or blame) for this. I have found no review of Martzy's now very much prized Bach Solo Violin Sonatas, on 33CX 1286/9, and only lukewarm praise for de Vito's Brahms Violin Concerto on ALP 1104. A very knowledgeable customer of mine, who was collecting violin music in the 1950s and 1960s, told me that the reviewers at the time had little respect for women violinists and thought the violin was essentially a man's instrument. We'd have very different views now! We now recognise what superb violinists they were, but their records are rare and hard to come by. Ida Haendel is another violinist who's recordings from the 1950s & early 1960s can be very rare. I've only ever had 3 copies of the 10" DLP 1190, Tchaikovsky Violin Concerto, Ida Haendel, conducted by Goossens, issued in 1958. The rarest de Vito, ASD 429, was not, however, simply a victim of poor reviews. The LP was withdrawn by EMI very shortly after it was issued as de Vito herself wasn't happy with her performance, so an incredibly small number were sold. In this instance it's the rarity rather than the quality of the performance that makes this LP so sought after.
The rarest item I've every had was DTX 191/7, which I sold for £8,200 eleven years ago. What's that? you may ask. It's a French Pathe issue, Mozart a Paris, a 7 LP set, conducted Oubrados, with outstanding soloists including Samson Francois & Lily Laskine.
Certainly not all very collectable records are rare. I could sell any number of copies of ASD 655, Jacqueline du Pre playing the Elgar Cello Concerto, coupled with Janet Baker singing Elgar's Sea Pictures both conducted Barbirolli, particularly the original semi-circle label in good condition. I've had over 60 copies through my hands. That is in high demand for a number of reasons. Jacqueline du Pre was an extremely fine cellist, who made a number of brilliant recordings in the 1960s. Her tragic later affliction, the Multiple Sclerosis which ended her career, perhaps makes the recordings she was able to do even more valued. It's modern reviewers and LP enthusiasts who possibly are responsible for the high demand for this particular recording, such as Art Dudley in Stereophile. He had superb taste and is sorely missed. Another recording much praised by modern commentators is SRCS 109, Malcolm Arnold conducting his own English, Scottish and Cornish Dances. Not a rarity, but hard to obtain as so many collectors want a copy.
The Absolute Sound magazine and the Super Disc List drawn from its reviews have a massive influence on record collectors. So a lot of records on the TAS list are sought after and command good prices. But there can be disagreement over what is genuinely on the TAS list. I use The Complete TAS Super Disc® LIST – compiled by Larry Toy. Larry tells me "The list was compiled from all the lists that founder and editor Harry Pearson (he used HP as his moniker) issued beginning in the early days of the Absolute Sound in the mid 1970's until a few years before he died (when he stopped issuing them). They include all of the records that ever were on the list, including quite a few that were on the list for a few years and dropped off. My list only goes through the time Pearson was alive and active. Harry Pearson did acknowledge me in one of the issues and thanked me for compiling the list." Subsequently The Absolute Sound have produced revised lists, adding some items and removing others.
You can find Larry Toy's The Complete TAS Super Disc® LIST as part of the Guide To Collecting. As you'll see it by no means only covers classical recordings.
The High-end Audio list of Supreme LP Recordings is another source of recommendations, though a very different one. The author says "The only qualification for this list is the sonic superiority of the LP, and NOT the quality of the music and/or the performance." Again some of the High-end Audio recommendations are sought after, and therefore become harder to find.