Monk heirloom pieces
Solution 1:
The data you request are indeed available, since the beta is already alive and kicking.
The monk will be a Leather wearing class, and in terms of Heirlooms it's going to share the gear with Rogues and Druids. Since you can be a DPS, a tank or even a healer, you have the following choiches (I've divided them in "healer/others"):
- Head: Preened Tribal War Feathers/Stained Shadowcraft Cap
- Shoulders: Preened Ironfeather Shoulders/Stained Shadowcraft Shoulders
- Chest: Preened Ironfeather Chestplate/Stained Shadowcraft Tunic
- Cloak: Ancient Bloodmoon Cloak/Inherited Cape of the Black Baron
For the weapons you can choose what you prefer. Monks will be able to use fist weapons, polearms, staves, 1h swords, 1h maces and 1h axes, with the ability to dual wield. As the Druids and Death Knights before them, they're going to be shieldless tanks.
- Healer Weapons: Dignified Headmaster's Charge (No good 1H+offhand alternatives, sorry)
- Tank or DPS Weapons: Burnished Warden Staff. Added in 5.0.4, it's available from the heirloom vendor in Dalaran for 3500 Justice points. It's equivalent in terms of power to the Repurposed Lava Dredger (without the fire resistance), but it's been added specifically for the monks, that cannot wield 2h maces.