Sort & Save… by subject and nationality. I snip the parts off the sprue (usually leaving a generous amount of the attachment point for speed and to prevent tearing out on the part). Put the parts in zip lock bags and label the bag with a Sharpie marker.
So, I have bags of Sherman parts in a box with other US kit parts, etc.
I keep track sets (indy link and link and length) bagged by type, one set to a bag, and boxed with other track sets (Fruils, Spade Ace, Master Club, etc.). So I have sets of DML Magic Tracks with other track sets.
I’ll occasionally bag and keep sorted individual sub-assemblies or alternate parts that are particularly interesting. For example, I have a No. 11 British radio set that’s quite nice that includes some PE parts that came as an alternate sub-assembly with the Riich Universal Carrier Mk. I kit. It’s complete and would go nice in any piece of early war British armor. Nice, complete engine kits for models that got their hoods closed up are also bagged separately. Things like that get a little extra TLC.
More “generic” stuff is sorted mostly like with like, so stowage and similar accessories are together, Jerry cans, crates, etc. Small arms are kept together, sorted by nationality and era.
Figures, for me, are mostly sorted by nationality and era, but things like heads and hands and all sorted together regardless of, say, any kind of head gear worn (because I’ll grind away hats and helmets and re-sculpt hair if I like a figure’s expression for some particular purpose).
Excess sprue, though, I put with all the other household plastic recycles. I will snip out particularly long, straight pieces for stretching, but I have quite a lot of that saved already over the years, so most sprue goes away. Same for kit boxes. If I need something for immediate storage, I’ll keep it, but the majority goes in the cardboard recycle.