Boxes are only useful after many years if you intend to sell complete sets. If you have kids playing with the sets, chances are the boxes won’t be very useful even if you intended to sell the lego in future. I’d throw 'em out.

Once a set begins to break down (either gets played with and breaks, or kid loses interest, or uses part of the set to build something else), I’d break down the rest of the set completely and add the parts to a pile for them to play with.

As for sorting… if all your lego fits into one of those containers, then maybe you don’t actually need to sort. Let chaos reign! Give your kids some direction - “can you build a house/spaceship/crocodile/alien?” and let them hunt for parts. Kids are usually more creative and build with what they have, so part discovery isn’t a bad thing.

If you really want to sort and make it more organised, with the numbre of parts you have, I’d just sort by size (small/medium/big pieces). digging through a big pile of unsorted lego for that small 1x2 plate is probably the most annoying thing for a kid.

Additional reading: https://brickarchitect.com/guide/

Hi! For kids, I like using medium tubs for storage. Smaller tubs for larger parts, and shoebox tubs for tiny parts and mini figs.

To help with the floor clutter, I converted an old wooden train table (check fb marketplace) to build. Instead of the storage bins, I was able to use two shoebox tubs and four of the next size up so stuff can be put away and covered. Then I found a medium tub that fit under the table for a big parts bucket.

This gives a place for builds to be put when play stops without worrying about them getting busted by being put in a large tub

I only ever saved boxes for sets that were well over $100. Everything else was recycled. Instructions are stored away in a filing cabinet drawer.

Edit: I just cross-posted something that was submitted to my old sub on reddit on storing instructions.

If you have the space, I highly reccomend a mat bag like this. They allow to spread the pieces out fully so you can see all of then at once, which is really nice for building.