Caravans generally screw themselves up and go bonkers when there's no depot on your site. Even a completely inaccessible depot will keep them sane, but a dwarven fort that does not cherish trade, that won't even build a depot in the first place? Inconceivable! What heresy against everything the traders' guild holds sacred! It's enough to drive an honest merchant insane!
Unfortunately, merchants driven insane by your anti-capitalist ways won't go away on their own, they'll just stay on the map until they perish.
I always spend the minute or two to sort through the trade orders. I generally order a lot of leather - a good material for most clothes, shields and bags; as well as some of the more precious gems (nice if you can get them included in moods), metal ores i don't have, flux stones if my embark is missing them (rare, but it happens), various colourful stones for colour-coded levers or special furniture, and usually the cloth types that can't usually be produced in large amounts locally, i.e. silk and wool.
If i feel like it, i also order a bunch of types of milk for cheesemaking.
I generally don't pay attention to the civ's desires. The various no-quality items generally aren't worth producing for export: who cares if yak hair threads are up 40% this year, they'll still only be worth 8 or 9☼ instead of six. Usually, some kind of craft or a common clothing item is also in high demand, and i'll happily take the extra haggling margin that offers, but don't bother looking such stuff up in advance.