It sounds like you're looking for a restoration (healing) spec. The classes capable of healing are druid, monk, paladin, priest, and shaman. Racially there aren't a lot of significant differences, though specific races can only play certain classes. (Alliance races are listed below as well, though the original question was about Horde)
- Druid (Horde: tauren, troll; Alliance: night elf, worgen) - limited to leather armor; tree form (cooldown ability) increases healing throughput; good profession choices: skinning/leatherworking, herbalism/(inscription or alchemy), mining/jewelcrafting
- Monk (any except Horde: goblin; Alliance: worgen) - limited to leather armor; use brews and teas as the primary basis of skills; similar professions to druid (I've never played a monk healer, so can't really address the specifics...)
- Paladin (Horde: blood elf, tauren; Alliance: draenei, dwarf, human) - can train to use plate armor at level 40(?), limited to mail previously; some people think they are limited to single-target (tank) healing, but do have some raid utility too; professions: any of the combinations mentioned above, or mining/blacksmithing
- Priest (Horde: any except orc; Alliance: any) - limited to cloth armor; best professions: tailoring/enchanting or herbalism/alchemy
- Shaman (Horde: goblin, orc, pandaren, tauren, troll; Alliance: draenei, dwarf, pandaren) - can train to use mail armor at level 40, limited to leather previously; can also use shields; in addition to direct healing spells, also have totems that provide passive effects and healing; professions: similar to paladin
For all, you can learn first aid, cooking and fishing as secondary professions that will come in handy.
Note that resto is much easier to level as primary spec now that you get access to the LFD tool at level 15. And, they're in big enough demand that you shouldn't normally have queue times that are very long.
ETA: Cataclysm/Mists updates
If we look at low level Rogue abilities such as: Sinister Strike, Backstab, Ambush, etc. We see a consistent trend of a percentage of Weapon Damage. Damage for these abilities is calculated:
base weapon damage + constant * (attack power)/14
In the case of daggers this constant is 1.7 and other one handed weapons 2.4. This is known as AP normalization. Additionally, only the main hand weapon is used in these calculations. As a result it is ideal to use a slower main hand weapon until you have sufficient attack power to influence your choice.
In the case of Rogues it is common to use Daggers as certain abilities (such as Backstab) require them. At latter levels you will gain other abilities which influence this selection (Combat Swords, Mutilate, Hemorrhage, etc), but at lower levels, slow Main Hand daggers is a preferred choice. A longer discussion of Main Hand weapon choices can be found here.
As a subtlety Rogue your "bread and butter" ability is Hemorrhage which does 110% MH damage (159.5% if its a Dagger as Daggers tend to be faster). I would suggest Initiative + Improve Ambush, making your combat look as follows:
- Ambush (or cheap shot)
- Gouge (later you'll use Kidney shot later in the order).
- Backstab (or Hemorrhage)
- Finishing Move
- Hemo -> Repeat till Gouge/Cheapshot come back up or you have the Combo Points to Finishing move
Garrote can be a good opener if the target stays alive for the full duration. As most mobs won't while leveling, Ambush is usually the better choice.
As a Subtly Rogue you also trade on Dodge, Ap, Crit and Armor pen (the last of which you won't get in bulk till much later). Keep in mind that Agility gives you 3/4, but is not as cost effective as straight AP due to Deadliness.
Source
Best Answer
Agility.
Agility is worth roughly two times as much as the next best stat for Assassination rogues.