Well, I collect records, although I do not care whether they're library recs. That may not fully count, but the point of records is the music, mostly, isn't it?
My holy grail is "Elemental Music" by Z'ev. It's the perfect piece of music, and if I had to choose among all the records in the world, this would be the one.
But I already own it. Ahem.
Regarding library records, I'm currently most interested in these two:
-- "Aurore" by Frydman & Cannone,
-- "Sfere Luminose" by Orlandi & Tonani (recently re-issued, so not a big deal actually).

A lot of the people "collecting records" today are ridiculous. Posers, strutting around on Facefuck and Insta with their Discogs purchases, looking for a profit of distinction. They've never been in a record shop. And Discogs needs to die.
What do I collect? I like good music, and I don't like bad music. So I collect the good music and pass on the bad. And I like a beautiful cover.
I'm not even sure if "collecting" is the right word.
I buy records, and then I don't throw them away. Just as I buy books. I've got many of them, and I wouldn't call myself a "book collector". If you now and then buy exemplars of a certain type X of object and don't get rid of them later, you're "collecting X", I guess.
Bargain bins are great! And fleamarkets. At least they used to be fun until Discogs -- which needs to die -- came along.
I realise that this hasn't a lot to do with library records. Confining myself to acquiring library records would be strange. But I'm very happy to be able to get to know so much great stuff through your forum. I imagine I'd enjoy going to a (library) record fair, which I've not done yet.