Hmm.
For a colorful army with Axe lords etc:
1. make enough copper weapons, shields, leather, chain and optionally plate armor. Forbid/dump all steel weapons.
2. draft dwarves, keep activated, assign them leather armor and shields and weapons.
3. Once each one has leather armor and leggings, assign them chainmail (they wear that over the leather) (I think/hope it adds to their armor).
4. set the military off duty. They will start sparring with weapons.
5. Every couple of months, set them all ON duty. Check each dwarf's inventory, looking for stuff in his hands. Sometimes they forget to drop something, and will wrestle. If a dwarf only has gauntlets, and his weapon and shield not both in the same hand, set him off-duty again to make him train weapons.
6. You will lose dwarves, that is, get serious injuries.
For a survivable military:
1. make armor
2. activate, have them put on chain over leather
3. doublecheck whether that former woodcutter is wielding a steel ax, if yes: m->w
4. set off duty
5. When they're mostly champion wrestlers, have them use copper hammers
6. Some of them will get a damaged spine/neck. If they're already good hammerers, make them train Crossbow. The rest go back to civilian life or into the guard.
7. Once dwarves who become legendary hammerers are fairly invincible. Now the trick is all in timing - I guess you want to avoid situations where dwarves with weapons they don't know well spar with inexperienced dwarves (i.e. dabbling shield users).
Did I forget anything vital?