I have a Goblin, Undead and Pandaren Mage; I’d prefer not to repeat specs between them but don’t know WoW lore well enough to determine which spec may best fit each race.
Any info./ help would be much appreciated. 
(This post also exists under the General Discussion forum.)
Goblins are known to be engineers dealing in explosives, so I think that Fire would be a good fit.
As for pandaren mage lore, they traditionally don’t use magic, and even advised the Highborne against using it by presenting them with a box of “all the magic they would ever need” - with nothing in the box. Arcane could be fitting in an ironic way.
I also really enjoy the aesthetic of Undead and Frost, it’s similar to death knights.
Another player replied to this thread (in the General Discussion forum) and concluded the same: Goblin = Fire; Pandaren = Arcane; Undead = Frost. I’m thinking that your matching answers settles the matter–unless someone else offers some compelling counterpoint. All in all, though, I think what you both have said makes sense.
Currently, my Pandaren’s Arcane, as I’m no Mage expert and want to survive in PvE; still, my goal is to play a different spec per race–even if that means many deaths for my Frost and Fire Mages–alas–as I level them.