Look over the new migrants after turning off Hunting, Fishing, Trapping, Fetch Wounded, and Feed Patients.
Skills first - if I get an expert in a field I need I assign him to that field, possibly bumping another dwarf to other duties. If he's the 2nd or 3rd in some fields I leave him there as a backup. At that point if I need an "apprentice" in a field I might put him there. Then I default on Engraving (only if I am still doing mass smoothing operations), Masonry, Furnace Operator, Weaponsmith, Armorsmith, and Architecture. Plus a sub-set of hauling tasks; like Wood and Stone, or Food and Refuse.
(This defaults him into my general labor pool and apprentice smithing program.)
Then I look at his military skills. If he has skills in a weapon he is added to a militia squad of his approximate level and weapon; e.g. a Level 5 sword dwarf migrant would probably end up in either a front-line or reserve unit depending on the age of the fort. If he is unskilled he goes into a Basic Training squad to start training in a weapon. If he joins a front-line unit he will train full-time or 9 months/year and have the better available equipment. Joining a reserve or Basic squad will probably be 6 months/year training, a simple uniform (cap, tunic, cloak, boots) with shield and a weapon. An "expert" in a civilian skill is probably put in a "cadre" squad where they do not actively train, but are issued simple uniform, a crossbow, and wood or bone bolts to use on the archery range in their idle time.
I don't consider any dwarf a waste. Just mis- or under- utilized in their previous employment.