Ok, first things first. You should be able to unlock retainers by now (Should have been shortly after the level 20 main scenario quest), and that is your main storage center. Each retainer may hold 175 items, and you may hire up to 2 for free, plus two more but at a slight increase to your monthly fee ($1 each as I recall). Inns do not allow storage of items directly, but do have a bell you can use to summon your retainer without being crowded by everyone else, an armoire to store certain specific items like achievement rewards or quested blue weapons and armor, a book to allow you to replay cutscenes, and a bed to enable unique login/logout animations.

Now, as for junk the market board is your best friend. Look up the item in question there, and see how much it's selling for. If it's SUPER cheap, or the same as what an NPC will buy it for, go ahead and just sell it to an NPC. Chances are the item is so common or unused that you won't fret over it. If the item sells for quite a bit however, you may decide to either sell the items yourself on the market board, or keep it handy (If it's expensive, it's either hard to come by, useful, or both). For the record, the vast majority of the crap you come across will be crafting ingredients. If you're not into crafting, then don't bother keeping them. Do keep any relevant food, equipment, or potions however.

One final note: If you may need an item down the line, but don't need it in the near future, consider selling it on the market board anyway. You'll enjoy the increased inventory space for now, and when you DO need it you can just buy it back off the market board. In a way, the game's economy can function as an unlimited bank storage, just with fees to use (sales tax) and a few minor inconveniences (Not always getting them in the quantity you want)