What type of heirlooms are worn by which classes?

You can basically just buy the heirlooms that have useful stats for your class. A thing to note:

Mail with Agility/Intellect and Plate with Strength/Intellect will change the armor type pre level 40

This means for Hunters and Shamans you can buy the Agility-Mail for example. They are Leather under level 40 and turn into Mail automatically once you reach level 40 with your character. (If you send it to another character that's lower than 40 you will get leather again). This of course works the same for Plate wearers.

Heirloom armors like the Agility-Leather however will not turn into mail after level 40.

You also have to know that the main reason why you actually buy heirlooms is not the fact that they scale with level, but rather for the Percentage bonus experience. This means you can also buy a Agility-Leather armor on Hunters or shamans for example. While you can also play with Cloth-Intellect on a warrior during the first few levels if you don't have the plate set, you should definitely switch to normal armor after around level 20 since it would take you too long to kill NPCs after this point.

There are eight sets of heirloom armour. Since patch 6.2, there is at least one set for each spec.

• Tattered Dreadmist: Spellcasting Cloth.

  Best for Priests, Mages, Warlocks.

  Suboptimal for Balance Druids, Elemental Shamans, Holy Paladins.

• Preened Feathers: Spellcasting Leather.

  Best for Balance Druids, Restoration Druids, Mistweaver Monks.

  Suboptimal for Elemental Shamans, Holy Paladins.

• Stained Shadowcraft: Agility Leather.

  Best for Rogues, Feral Druids, Guardian Druids, Brewmaster Monks, Windwalker Monks.

  Suboptimal for Enhancement Shamans, Hunters.

• Mystical Elements²: Spellcasting Mail.

  Best for Elemental Shamans, Restoration Shamans.

  Suboptimal for Holy Paladins.

• Hunter Loot^{2 4}: Agility Mail.

  Best for Enhancement Shamans, Hunters.

• Burnished Might³: Tanking Plate.

  Best for Protection Warriors, Protection Paladins, Blood Death Knights.

• Polished Valor³: Strength Plate.

  Best for Fury Warriors, Arms Warriors, Retribution Paladins, Frost Death Knights, Unholy Death Knights.

• Pristine Lightforge: Intellect Plate. Added in patch 6.2

  Best for Holy Paladins

<sup>1. Holy Paladins do not have their own heirloom set. No longer true as of patch 6.2
2. Will become leather for Shamans and Hunters below level 40.
3. Will become mail for Paladins and Warriors below level 40.
4. There is no single name for this heirloom set. The name refers to the tendency of Hunters to use Strength mail items simply because they can use it, as evidenced by the Raging Berserker's Helm and Herod's Shoulder.</sup>

After quite a bit of research I have found that sending Plate heirlooms off to a Paladin or Warrior will change them to Mail until the character can wear Plate, then it will be converted back to Plate. This only applies to this scenario, and for Mail for Hunters and Shamans.

Below is a list of Classes by armor type (the heirlooms work the same):

Plate:

1. Death Knight
2. Paladin
3. Warrior

Mail:

1. Hunter
2. Shaman

Leather:

1. Druid
2. Monk
3. Rogue

Cloth:

1. Mage
2. Priest
3. Warlock