I guess the modern fiction stuff; there should be enough of that for a while, and there's a decent chance there are digital copies that could be reprinted.

If that runs out, keep going from newest published backwards, minimising how many older books will need to be burned.

Any religious books. Then any boring non-fiction books. Then probably like, idk, 50 shades of gray. Also history books, cause idgaf abt history personally nothing that interests me xP

Also good for me, I live in a place it never snows.

Burn the religious books first. Besides that, I don't know, except burn the fiction before the nonfiction. (Not that I think fiction has no use.) Really, though, I wouldn't care, because all of those books are available elsewhere.

Start with duplicates and replaceable books. The archives, with all their irreplaceable primary sources, must be protected at all costs, even possibly freezing to death. Within replaceable books, the fiction section can go first, not only is most of it replaceable but it's also expendable, as I can get my entertainment elsewhere. Then redundant translations of foreign texts, at worst they can always be retranslated.