Unique, set and quest items do not show up in the trade window in the act they are found, and can not be given to a summoning doll. Once you move to the next act, unique and set items will be renamed (though keep their stats) and will show up in the trade window to be sold, if you wish to, and can also be transferred to a summoning doll.
Summoning doll inventories remain when they are killed or unsummoned, so are a great place to store most loot (especially since the 1.47 patch).
Barrels only started being locked with the 1.47 patch, which fixed the previously broken Lockpick skill.
