I'm a big fan of the "Hunter Militia" strategy. You can't arm your entire fortress until your wildlife situation allows it, but 20-30 dwarfs with crossbows will fix pretty much any wildlife situation in very short order.
My starting strategy is to make 5 of my starting 7 hunters (miner and "time-sensitive agriculturalist" [animal processor/farmer] exempted from duty). I'll usually take all but 1 off hunting duty right away, but once the first wave of immigrants arrives I switch the 5 back on, the first 5 of what will eventually become a fortress-wide militia (miners and farmers exempted.)
The advantages of a militia are many:
Also, keep in mind that if a tantrum spiral starts, and you have ALL your dwarves armed to the teeth... things will go downhill even faster
"An armed society is a polite society."
-Robert A. Heinlein
I've never had a tantrum spiral -- knock on tower-cap wood -- but I've had a few tantrums, and instead of the berserk offender killing a bunch of his former friends and kicking off a tantrum spiral what tends to happen is he gets cut down in a hail of bolts the second he goes crazy, and the situation soon stabilizes.
Kobolds and snatchers fare poorly as well. They invariably wander into high-population areas and find themselves surrounded and shot to pieces once discovered.
Ambushes are handled particularly intelligently: the dwarf under attack, being a civilian, runs away, and being a hunter, fires his crossbow. Who could ask for more? Your civilians armed or not will tend to draw the ambush toward your military as they flee, but I've seen entire ambushes defeated by a single fleeing dwarf.
The final advantage is armor. Leather armor is cheap, doesn't seem to hinder mobility or productivity, and protects your civilians better than just clothing. Civilians with the hunting occupation will wear leather armor all the time.
A word of warning, which others have mentioned here: never make waterskins, and destroy any you come across. You want your militia drinking booze, and if they get their hands on a waterskin they'll only drink water.