World-of-warcraft – What happens with race-rep when you racechange

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

Short answer

It depends. Here's a quick sheet based on my experience if you'd rather not think too much about the options:

• If your goal is to PvP, it's pretty even between Goblin, Tauren, or Undead. Personally, I'd probably go Goblin.
• If you want to be an enchanter, roll a Blood Elf.
• If you want to be an alchemist, roll a Goblin.
• If you want to be an herbalist, roll a Tauren.
• If you don't want to be any of these professions, roll a Goblin.

Long Answer

Race differences are pretty negligible. Any race can be an effective priest. What it usually comes down to are the professions you want to roll and whether you are going to be a raider or a PvP player and how much fun you'll have playing the starting area or simply walking around looking like a member of that race.

That being said, you have 5 options as Horde. Here are their noteworthy abilities. I don't bother mentioning things like resistances or extra time underwater as they really aren't all that helpful overall. I already indicated my opinion above, but depending on your personal preference (maybe you really hate being feared and favor an Undead for their ability to break fear effects overall), the lists below may guide you in another direction.

Blood Elf

• Bonus to enchanting. Since tailoring/enchanting is a good profession combo for a priest, the bonus will help slightly in leveling your skill.
• Free silence/PvE Interrupt/mana restore.

Goblin

• Bonus to alchemy. Herbalism/alchemy is another good profession combo for a priest.
• Free "disengage" (blast away from enemies).
• The rest of their racials are worth mentioning when combined: cheaper vendor items, access to your bank from anywhere, and faster cast times.

Tauren

• Bonus to herbalism. Herbalism/alchemy is another good profession combo for a priest.
• Additional health.
• Free AoE stun.

Troll

• Temporary casting speed increase.
• Shorter snare effects.
• Slight health regeneration.

Undead

• Free quick heal after combat.
• Free "Charm/Fear/Sleep" effect interrupt.