I feel your pain, I had to do the same thing. When we retired the two of us moved from a 4,000 sq foot house to one with 1,600 sq feet (and no storage except the unconditioned attic and the wet basement, so no books there).
Since I couldn’t take everything with me, I decided to radically downsize. I took my magazines (all boxed), but donated the entire bunch to our Universities Special Collections group -- complete Fantasy and Science Fiction, 45 years of Astounding/Analog, 45 years of Locus, Galaxy, Asimov’s, etc. Total was over 2,200 volumes. I didn’t cherry-pick, but occasionally wish I had (the Dune Analogs, The Cordwainer Smith stories in Galaxy, ...). But they went to a “good home” that will protect them, and make them available.
For my paperbacks, I started at both ends. I pulled the “must keeps” — Cherryh, etc, and set aside the “ok to go” (which ended up being a lot!). Then the hard part, the middle books. I let my mood guide me, and split those up. Then I boxed it all up. The larger part (dunno how many but likely 2-3,000) went to an old friend that is a sci-fi/pulp dealer. He sells them as he can, and I get books from him, so good deal for both of us. I ended up with my favorites and “the best” books. I counted the other day, and it came to 2,000 sci-fi and a couple hundred others.
Since then, I confess to retrieving some of my books from my friends stacks. It’s not uncommon to see a book come up in discussions, and think, “oh, I had that one”. But I’m content, and in my situation I didn’t really have a choice to keep everything, so the great purge was easier because of that. These days, I read and buy more that ever. Lots of kindle books, which are great for “read once” books. I started back into limited editions (Subterranean, Centipede, Suntup, etc), which are expensive, but are lovely volumes. Some of them, the Suntup in particular, are astounding things to hold. Quality over quantity !
PS. I kept most of my Poul Anderson books.