This discussion is designed to show other players and ZoS developpers what players do at Veteran level to store the items that they want to keep.
With all my characters, I currently have 1426 inventory slots, 1092 of which are being used.
I'm sure everyone has their own method but nobody (or almost nobody) is doing it without mules after reaching vet content and crafting a bit.
Here's mine:
Character #1, VR14, trials and endgame content, 70/170 inventory.
Mostly alternative gear, potions and food, with also some materials and fishing bait that I'm likely to encounter.
Space is required to easily switch to a Light Horse for speed runs and still have enough room left to collect drops.
Character #2, VR7, currently leveling Cadwell's Gold, 84/170 inventory.
This one still has potions and food, but no alternative gear. He also carries my somewhat useless provisioning materials (tier 4 and below) that may or may not become useful again with the provisioning revamp.
Again, a lot of space is required to collect drops without banking too often.
Character #3, VR3, currently idle, 140/170 inventory.

This one carries my useful provisioning materials (tier 5+) that haven't reached a full stack yet, as well as Treasure Maps (yes, I collect maps).
The space left is only used for crafting (all 6 professions).
Character #4, level 10, full-time mule, 113/165 inventory.
This character carries the gear that I consider "precious": mostly bound equipment from trials and dungeons, but also the old lvl3 rags from the prison in Coldharbour (maybe used for roleplay one day).
Character #5, level 9, full-time mule, 155/155 inventory.

This one has different kinds of items:
- 1 stack of each style material
- 1 stack of each of the veteran materials in wood/bs/cloth, with 3 stacks for VR10+
- 1 stack of green, blue and purple upgrade materials
- several stacks of gold upgrade materials
- the gear I use to level alts: full setup (10 items) at level 10, 20, 30, 36, 46, VR1 and VR4 so far
Character #6, level 6, full-time mule, 82/122 inventory.
Stacks of flowers.
Character #7, level 6, full-time mule, 130/134 inventory.
Stacks of provisioning materials.
On a side note, if I crafted all the purple food that I could right now, with over 1000 tomato/oats/pepper combined, I would reach 10,000 hours of game time with food buff on. I think something's quite wrong here.
Character #8, level 6, full-time mule, 91/100 inventory.
Collectibles, pets and Costumes, with some fish bait.
Bank, 227/240 slots.

Mostly:
- all flowers that haven't reached 1 full stack
- crafting materials in BS/Wood/Cloth
- style materials (everything above 1 stack gets deleted)
- some potions and items being exchanged in between characters
Total: 1092/1426 slots.
I'd love to play how I want without using so many mule alts and spending so much time organizing my inventory but I simply can't.
Of course, changes are coming with update 6 for Collectibles and Pets, but I think the inventory system requires deeper changes.