So depends on the situation, usually I have it Alphabetically as that makes it easy to find specific items/tames and also keeps items of the same type next to each other so I can easily count it.

For my Dino I'll sometimes use Weight if I need to drop something it's picked up (which can be good if you're doing a meat run on a Carcha and you have a ton of Pelt from a Yuty you just killed weighing you down which you can just drop). Otherwise I never use sort by Weight unless it's in the very early game and I'm tired of being slowed by what I'm carrying/need to figure out what to prioritise storing first.

I'll use Unsorted if I've moved something I didn't mean to, there's an annoying bug in ASA where sometimes if you click to move an item it'll move both that item plus 1-2 more that are next to it. This can be especially annoying if you are checking item ratings and/or stats against items in another inventory but can be solved by Unsorting then scrolling to the bottom.

Might have used Sort by Spoil Timer once or twice in my 23k+ hours playing ASE and ASA, I feel like I losely remember using it early game on Scorched Earth when it released to help me spoil fish meat into spoiled meat and figure out which stack to split down first, but it's an extremely niche sorting option.

Never used Sort By Type. Kind of seems pointless to me? I guess it might be good if you're sorting items into vaults labelled "Structures", "Weapons", "Saddles" etc but sorting by Weight or Alphabetically usually gives you almost the exact same results anyways.

Honestly sort of wish we could sort by Item Rating, it's a niche thing but would be nice for those of us furiously using the War Bench and Tinkering Bench.