The military.
Simplified.
Usually it's more like this..
But on a serious note:
-Absolutely make a custom uniform that covers every inch of recruit in about 3 layers of steel
-Divide your melee dwarves into 'training' squads of ~2-3 dwarves each, with all dwarves in a given squad using the same weapon, with minimum training number set to 2 either way. It encourages sparring (good for noob recruits) instead of demonstrations (waste of time if recruits are doing the demonstrating)
-Send them out to kill random wildlife
-Capture some goblins with cage traps (I know you don't like traps, but bear with me..) and arrange an arena fight vs. your recruits. If you want to be hardcore about it, leave the goblin his weapons, and just use the trap/arena as a way to ensure your recruits have a fighting chance against a single goblin rather than getting overwhelmed by a full squad at once. If you're willing to cheese it a little, strip the goblin of all equipment (unforbid and dump while he's still in the cage), then set your recruits on him with wooden training weapons, he'll take forever to die and they'll get plenty of skill.
Of course, that's assuming you're set on melee dwarves. If you want to go marksdwarf-heavy, all you need is a drawbridge and fortifications, they can train "on the job" so to speak by taking potshots at the next goblin siege. The skillups are better than archery practice if you can actually get them to stand next to the fortifications with ammo, and they're
relatively safe. If you set it up so that nothing can stand just outside the fortifications (either via a moat or putting them up a z-level) then only elite goblin bowman can hit them (watch out for those guys, one
will slaughter your entire noob marksdwarf squad).
If you're like me and you must defend your fort the hard way, no traps, no danger rooms, no raising the drawbridge and letting marksdwarves whittle them down, then positioning is critical. You want to station your barely-trained/equipped dwarves somewhere that the goblins have to come to them one by one, say a 1-tile hallway leading to a larger room where your squad waits, with some way to block off the hallway until your dwarves are ready. Like so:
XXXXXXXXXXXX...
...D.XXXXXXXg..
<- Fortress .D.D.+.g.g.g.g. Outside ->
..D.DXXXXXXX.g.
XXXXXXXXXXXX...
D = melee dwarf
X = wall/rough stone/whatever
+ = door (keep locked until your dwarves are in position)
g = goblin ambush squad
I've actually defeated ambushes without losses this way, using only skill <4 recruits with just weapons (no armor/shields) and a lot of luck; it won't do for sieges, but it'll get you through the first year or two until you have a chance to get their skills/equipment to decent levels. It should go without saying that, for this to work, you need to spot the ambush before it's in the middle of your fort slaughtering civilians - for this I use watch animals (preferably useless pets) penned at strategic points on the map.