There's been quite a lot of concern about the limited amount of storage in the game. Here are some workarounds.
1) Upgrade to Silver. For a one-off $10 payment you go from 2 bag slots, 2 bank slots and 2 house vault slots to 3 bag slots, 3 bank slots, 2 shared banks slots (extremely useful for transferring items) and the 2 house vault slots. As Silver brings other benefits too it's worth it if you're going to spend some time in EQ2E.
2) Get really big bags. The biggest bags are, I think, 44 slots (T9 rare). These are available for Station Cash but you can also get them from player crafters in game. 150 Station Cash ($1.50) gets you 10 goes on the Broker, or you can look for bags on the broker just to see who made them and send that person a tell.
3) Boxes are just as good as bags. Boxes are now weightless meaning they are functionally identical to bags and the same size as the equivalent crafted bag.
4) Make your bags/boxes. Any T2 Outfitter or Craftsman can make 12 slotters using common materials or 16 slotters with a rare. A Carpenter or a Tailor can make much bigger ones.
5) Make mule accounts. There's no limit to how many accounts you can have so doing things like making 9 accounts for harvestables, one for each Tier is perfectly feasible. To mule you either need a friend to hold the items for you or to multibox.
6) Use your mules' Overflow. When a character's inventory fills up excess items go into overflow. A character is quite limited while he has items in overflow - he can't craft or harvest - but that doesn't matter on a mule. There doesn't seem to be a limit as far as I could see, I could keep trading items to him (so multibox or a friend's help is required).
7) Use your guild, donating is better than deleting.
8) Make a guild for your alt. It costs $10 for a guild charter and you need a silver account so a total of $20 has to be spent for you to do this. You only need this on one account, your legions of mules can stay Bronze and completely free while joining your private guild. You can store a lot in a guild. Unlimited cash to start with. There is a guild bank, it's basically 4 extra bags that grow as the guild grows. If you get your alt's guild to 30 you can put in guild hall amenities. These include automated harvesting bots that go out and harvest for you and a massive harvestables storage unit (150 types, up to 20K in each stack). There's an ongoing rent for a guild hall, I don't know how hard it is to keep up with if you have a high level character but I suspect it's not very hard.
9) Get a bigger house. House vault in bigger houses can be up to 6 slots (but the rent is higher).
10) Transmuting is both useful and saves a lot of space. (WoW players will know the concept as disenchanting).
11) Cash can (currently) be stored as high level fuel which is both expensive and sells back to NPC vendors for the same price that it costs. This may get altered by the developers but simply invest in some other commodity (eg rare harvestables or master level spells). In fact by "storing" your cash in commodities that trade on the player market you should be able to turn a decent profit, buying Masters when no one is interested in them and selling them on at a premium.