My plan is to get the fort into a self-supporting state and then work on a military and some mining operations. What kind of minerals/ores/whatever they are should I be hoping to stumble upon?
Iron bearing minerals mostly, since iron = steel, and steel = best equip you can make besides Adamantine stuff.
Here's a brief summary of what kind of rock you should dig into to find iron
Iron ore is found in sedimentary layers and igneous extrusive layers. Andesite, Basalt, Felsite, Obsidian, and Rhyolite layers are igneous extrusive, while Sandstone, siltstone, mudstone, shale, claystone, rock salt, limestone, conglomerate, dolomite, flint, chert, and chalk layers are sedimentary.
And, the names of the three iron-bearing rocks
Iron occurs naturally, and can be achieved from any of three separate ores: Hematite, magnetite and limonite.
You should also look for Basalt, which contains Platinum veins, gold and copper. You can train your armorsmiths and weaponssmiths by making Copper Helms and copper weapons (1 copper bar cost per helm, all weapons cost 1 bar as well), and then re-melting the products. Gold and Platinum are just really shiny and nice.
Something I usually do is have atleast 2 or 3 miners mine a network of tunnels spanning entire Z levels. Then I just micromanage the rest of my dwarves while waiting for my miners to uncover the goodies. A positive side effect of this is that Strange Moods occur allot more often depending on the amount of squares you've mined, and strange moods can lead to some easy Legendary dwarves.