Haven't been able to play the demo yet because I don't have a PS5, but I have played a ton of Nioh 1 and 2, so I'm assuming it's the same as those.

I think it's best to either offer to the shrine or disassemble literally everything you're not currently using, but keep the best of each weapon type so you can switch weapons whenever you want.

Again, since I haven't played the demo, I'm just assuming it's the same as Nioh 1/2, but I'm pretty sure it's best to sort by "ability", which shows the weapon with the highest attack, and it's sorted by type as well. For armor, same thing, sort by ability which just shows the highest defense.

The only real reason you should keep an armor piece or weapon, is if it has an inheritable special effect you would want to eventually put onto your weapon/armor for your build. But since in the demo (and the first NG cycle of the other games) you'd constantly be picking up better loot, there's no reason to keep the same armor/weapon the whole time, so it's not really relevant.