Those Hirelings are also known as Mercenaries. As listed on Diablowiki.net only the weapon and off-hand slots have restrictions as followed:
Rouge Scouts (Act I)
- Only Bows (NO Crossbows or
Amazon only
Bows) - can use Cold Arrow or Fire Arrow in addition to Inner Sight
Desert Mercenaries (Act II)
- Spears, Javelins and Polearms (no
Amazon only
equipment) - use Jab Attack and have a Aura dependent on type and difficulty they were bought in:
. |Normal/Hell|Nightmare | Combat |Prayer |Thorns | Offense|Blessed Aim|Might | Defense|Defiance |Holy Freeze|
Iron Wolves (Act III)
- Shield and Sword
- skills depend on type:
Inferno or Fireball for Fire
Glacial Spike, Ice Blast, Frozen Armor for Cold
Charged Bolt and Lightning Bolt for Lightning
- they will not hit much with the sword - look for caster-bonus on it (for example,
Spirit
runeword)!
Barbarians (Act V)
- Barbarian class-specific items, one sword (no dual-wielding)
- use Bash and Stun
Additionally to the type restrictions, mercenaries follow the items requirements for Strength, Dexterity and Level. Back when I played Diablo II, act II Mercenaries were the most common choice due to their buff-auras.