When I get to know the Liason offers (seeds at 200%? - I can spare some of them; gauntlets at 150%, I'll bash some up...) I set some of the stockpiles to the relevent things I'd like to offer. Generally laid out in 1x11-tile strips (in 11x11 rooms, the way I plan these things) each dedicated to one narrow type of good, initially just one bin, if applicable, and if it visually fills up (from natural or forced movement) then I happily adjust accordingly.
The same with figurines, rings, earrings, amulets, bracelets, crowns, and scepters (regardless of specific demand) and Large Gems. If there's no demand this season, there may be in a future one, and rock-crafts handily eat up any surplus of a boring-stone-type (if I have wooden things, probably elf-bought while offloading surpluses, they get their own piles, just to avoid accidentally insulting the elves themselves in a future mixed-goods swap).
When the traders are announced, the tradeables are handily near to the Depot when selecting them to be moved there. Saves time as mandorfpower diverts en mass to haul everything there, and with the selection of goods (with or without other filtering, any item or bin within single-figures-or-so is probably what I want there, I barely have to check the bin contents). I haul bins as much as possible, though never export them, nor bags if I can help it, though will import bins-of-stuff sometimes more for the bin. Bags too. And barrels, except for the ones of blood. But individual items don't cost much more time if nearby like this.
I should have a good stock enDepoted by the time the incoming goods are unpacked. If I have some high-importance items still stuck many Z away, and maybe a way bit off in X and Y too, in my magma-workshop area that never got them into the pre-trade prep area, I can speed up those by exploiting Dump mechanics to make them a priority/sole job for some selected free bodies to undertake, into a special Refuse zone put close to this other action.
As I've traded, if I've time while waiting for some excellent-quality rings (made since the initial arrival), or somesuch, and have other hands with nothing much important to do, I might check the traded-for goods in-depot and make the trade-out stockpiles, now empty, their perfect recipient (and/or that Refuse staging spot, for things I won't have trouble with spoilage). Clear the stuff out, plus de-Mark For Trade all now-empty bins and maybe mark for Dumping to shuffle them out of the place too. Makes it easier to see what's left as I eke out as much bartering as I feel I need to.
I try to leave nothing still Marked For Trade by the time they pack up, one way or another, and then I've got a little bit of shuffling of trinkets bought from these traders (like items only bought because they fulfill the next Dwarf caravan's idea of being wanted) into the nearby stockpiles, or ultimately further into where I'll find them useful (foods to a central foodstore, bars to near the forges, etc). But, especially if I'm Turtling for the winter, or likely to for any other reason, the Depot is emptied of remaining/remaindered items as much as possible, plenty of time to prep for the next visits...