LP collection

CLassical do not have the money in them Jazz or Rock stuff does. Since it is all early 1950's it is all monaural
I assume it is sorted by composer.
The fastest way would be to sell groups of records.
Break them down into batchs like Beethoven String quartets,
etc.

Then when you say extensive? Do you mean 1,000? or 50,000?
If NO-ONE has skimmed off the best, certainly some valuable records in there. but not too many.
If any professional has skimmed off the top/most valuable 5%/10%.. then your records are worth way less.
Classical mavens will disagree, but Classical music is dead in the water. So the headache of selling them to maximise profit may not be worth the bother.
Auction is the only way to sell if you do not know the values of each item. Let the market sort the prices.
The one group of records with the most potential with a one sentence comment is RCA shaded dogs. Though monaural are worth less than stereo.

If you got a bulk offer of $0.50 per record with them picking them up, you should grab it.
Otherwise start using a camera and posting them one at a time on eBay... or here. biggest 'set' worth trying to auction at a time would be 20, with pictures of the covers for eachauction.
So you see it is time intensive to actually sell them separately.
Finally, what looks mint to an untrained eye may be totally worn out junk to a pro. Not saying you do not know, but PLENTY of folks don't. And a perfect record is worth many times what the same scratched up one is

You mention "early 50's" - it would be helpful to know how early (or late), and what labels you have. Are they actually all mono, or do you have some early stereo records (which would take you into the later 50's)?

Overall, I think Elizabeth offers some excellent advice. If it were me, I would go through your collection and pick whatever records you think are worth the most. Just put a few on ebay and see what happens. Use the results to help figure out how best to sell the rest of them.

If I were you, I would at least take some time to educate yourself on which of those records that you have may be very valuable - you could indeed have some real gems in there. If you just want to get rid of all of them quick, then Elizabeth's advice is good. However, if you really do have some that are worth quite a bit, you will want to sell those individually for sure. Also, bear in mind that most classical music lovers usually tend to like buy things individually, and will often pass on bidding on a big group of things. You will certainly make more money on them in the long run if you sell them individually, though this is a great deal of extra work.