Aye, your first caravan will always be hte dorfs who will always strike trade agreements up (renewed every year). Elves and humans will come next. However, if you start at a non-standard embark time you can get the other caravans first. I've embarked in the winter and found an elven caravan before dorf one.
Also, the different caravans bring different stuff. Dorfs will generally carry the same stuff you could embark with, but they usually "generate" other metal items to trade that you couldn't select on embark. Humans will never have steel and will bring "large" weapons and armor that you dorfs can't equip. You can still buy these and smelt them down for metal (along with the kitchen knives and other human metal goods). Elves will only bring wooden and cloth/leather items. However, they will also bring domesticated exotic animals. You can get breeding pairs of dangerous war-beasts from the elves if you are lucky. However, the main use of hte elves is if you start in a wood-poor environment (glacier, wasteland, desert, badlands, evil bioimes). What little wood you get goes to beds. Then you trade for wooden barrels, crutches, splints, buckets, etc from the hippies. All caravans will bring food as well.
You can use most human weapons, just not the ones like mauls, two-handed swords, great axes, that kind of thing.