Characters can find their own specific weapons and/or items (ie. whatever they might have been using prior to their arrival) in the weapon shop or the item bazaar, respectively. Any weapons/items with certain unnatural powers (ie. changing time or their environments) will have been stripped of said powers and reduced to that of their normal, every day counterpart. Most of these items will be handled on a case-by-case basis, depending on what powers they possess. For example, magic wands or the pins from The World Ends With You still work, but Link's ocarina would not change time, though it could still play prettiful music.
As stated in the FAQ, character's clothes are brought to Luceti with them; they can appear with the character upon arrival or in the clothing shop within a few days. Clothes are either left unaltered or cut to provide holes for the wings as per the players wishes.
If you have a specific article of clothing or item that you are not sure will work or is even allowed, please ask a mod.