I bought a few plastic storage bins on Amazon, but you can get them anywhere, and the dimensions are listed so you can pick the appropriate sizes. I categorize them very broadly (e.g. tech, clothes, miscellaneous, etc.). Whenever I'm trying to clean and I get overwhelmed or run out of time, I put the remaining items in the relevant bins, and then put the bins out of the way in the basement.

That way, I don't have stuff sitting all over the floor, and I know where to look if I can't find some random thing. Limit the number of storage bins you have, or else things will get all disorganized again. Sure, the items inside the bins are in a mess, but I can close the lids, put them in the basement, and forget about them unless I need to find something. Additionally, keeping the items in plastic storage bins makes it easy to move if necessary, since you don't have to box up all the assorted items into cardboard boxes.