I'm going to make a video about trading in DF soon, so I thought I'd run some of my ideas by you guys to see if I left anything out / got anything wrong.
Here's everything I know about trading in no particular order
If you focus on trading slightly more than usual you can have more to trade with the first several caravans. This can get you more food, more of whatever you don't want to make yourself. In some places this can be extremely handy, such as those without wood, food, sources of leather, metal, etc.
If you're going to try to trade more than usual it helps to start with dedicated traders. Having some level of skill at appraisal is necessary. I usually make a trader around Competent at it. Judge of intent can tell you how the traders are feeling, if they are happy or getting mad.
The material of trade goods maters. Marble or any other of the flux stones is worth more in trade goods. You can make extremely expensive encrusted trade goods by deliberately mining out all the gems you come across and keep a setter and cutter busy. Eventually they can make nearly artifact quality items by doing the same trade goods over and over. When you have a couple each of cutters and setter you have a fair shot at a fey mood and getting a legendary. Legendary cutters and setters make extremely expensive items.
Metal is even better than stone when it comes to trade goods. Clothes from dyed cloth is more expensive than just clothes. The ultimate expensive item to sell is an adamantine spiked ball, but I wouldn't sell those until you made as many weapons and armor as you wanted first.
I like to trade for things I'm too lazy to make myself or are hard to farm / get in a fort like enough leather. I don't like to trade for anything I can make better versions of like armor and weapons. I do buy raw ingredients for food. Selling high value cooked meals is one of the easiest ways to get a lot of money from trades. I like to buy animals to turn into food and leather. I buy leather, books for fun, parchment because getting enough can be a pain. I buy clothes and armor for the humans in my fort so I don't have to make it myself or as often. I buy musical instruments because they are so complicated to make. My favorite thing to trade for is giant animals from the elves.
I don't hear this get talked about a lot, but if you give any of the traders a lot of profit, like double or more, they bring more and more stuff up to a certain limit. The humans and dwarves will bring you pages of stuff on their wagons, pages of meat or parchment if you ask for it. The elves will bring about up to 3 times their starting amount, which is still just not that much.
They can only carry so much weight of stuff away. If you sell them trade goods in bins they pack the bins up and leave faster. The world is a dangerous place. I usually put my trade depot underground with routes to it from the edge of the map. Pro tip - the route needs to be direct or they will pick one that seems strange to the player. Since this is a way in to your fort there needs to be a drawbridge between the trade depot and the rest of the fort to close during invasions. Since you can bring the merchants to you and put them where you want, why not make it close to your main stairs, and put stockpiles for trade nearby.
Things I like to sell: trade goods, used clothes. For the first caravan whatever we made that they like - any expensive shields, beds. I don't usually sell prepared meals because like a lot of people I feel they are a bit OP, but for that first caravan I do sell whatever we have, because we can buy far more raw ingredients from the caravan and more than make up for it. I usually make a dedicated stone crafter or two in my starting 7, and one gem cutter and one gem setter, different people. Why not make nicer more expensive things right from the start? To keep three crafters shop fed for stone I set up stockpiles with lots of wheelbarrows and have most of the fort enabled for stone hauling.
In my experimental trading fort I had one crafters shop constantly making stone pots for all the food and booze we were making, and two for making the two kinds of trade goods the dwarven liaison had ordered.
I don't usually pay attention to what they are asking for unless they are paying 180 or 200 percent more for it. In this case they wanted rings and crowns, so I switched from making any trade goods to just those for a year.
Currently the option for more trades in DF hack lets you ask the humans for what you want to trade, so you can at least ask for more of what you want.
So, any suggestions? Anything I completely left out?