[Pale_Horse]

I would like it to be along the lines of a NPC in the town(s) that they can hold your unused gear for a cost. Look at it like a bank, you have no room to keep your gear so you hand it over to a merchant to store, then when you want to take it out their is a small charge in gold.
Any character within the same account can scroll threw the items held by the NPC and choose what item to take out. On the otherhand, if you want to xfer gear to another account you can simply type in your account name and password (same as logging into bnet) of the other account. Drawback is, when the account is deleted, so is the gear from the NPC banker, same as if you were to delete the account manulally without xfering the gear, you would loose all said gear.
Another good feature as stated before, have the merc be able to carry some gear, as well as pots so it can heal itself as well.
Now every good thing will have it's drawbacks, and these should be, that the NPC merchant that holds gear, can only hold a certain amount, that increases with overall account lvl. So, someone who has 1 lvl 99 character and the rest that are lvl 1 can hold less then someone who has all lvl 80+ characters. Look at this the same as your gold carry capiblity which increases with lvls.
Quests to increase inventory size is a great idea, but IMO I think this would suit the merc better, to finally match the inventory size of your own character in the end.

Now the vendors, they should cater to the character class you are using at the time. Case in point if it's your first character, as a a Paladin, who wants to see a vendors inventory full of sorc orbs.
Another option is, to have a choice to see items geared to a perticular class. This could be done as easily as having a seperate tab when chooseing to speak to the Merchant. This would in the long run, allow for less NPC's in towns to run to when needing items.
Another idea, maybe not as good or fine tuned, would be to have a NPC merchant in town, that would actually go and trade for you. You will state what item you are looking for, and what you are willing to pay. If you find the item you want the NPC will notify the other player of a offer. You can then look at the item threw the NPC inventory, and choose if you want sai item. This would cut down maybe even eliminate trade scams. This would also stop the missing out of trade games since you do not need to change rooms. Possibly even eliminate trade games intirely to make room for other questing and lvling games.
Another option would be to have a quest to save someone who later becomes a thief in each town area, this NPC will get you anything in any other merchants inventory within that town, for a price.The price for such items will be random, such as gold, pots, gear, maybe even a side quest for a item. This could be cheaper in the long run, or could even make things difficult for you.