I find it pretty rewarding to run as many industries as possible in a given fort; it gives your dwarves something to do and fills your fort with masterpieces. It always makes me a bit sad when an industry is impossible (e.g., beekeeping on a glacier), but I'll go out of my way to purchase sand or clay if they aren't available on the map. Later in a fort's life, I even like to allow a single dwarf to become the designated Trapper--there's no real need to capture, tame and sell/extract from vermin, but I like that the option's there. I've never delved into dwarven computing, just minecarts in general and power generation.
As far as the military goes, I find just about all the options to be really useful--if you set up rotating patrols around your various gates into the fortress (I prefer to have squads go on patrol duty the month before their yearly vacation), you don't have to worry about, say, manually un-caging captured blind cave ogres for them to slaughter in the arena, they just take care of 'em in the cavern. The one exception to all the options being useful is my favorite mechanic to ignore: lawdwarves. Seriously, those brutal pigs have no place in my forts. I'd much rather a noble have a sad thought than a useful craftsdwarf be crippled or killed because I forgot a mandate, and when it comes to actual criminals, like vampires, I'm much better at actually ridding the fort of the menace by means of traps than they are by means of beatings.