What is the best character to go with a goblin rogue and an orc shaman in WoW

It depends on what you prefer to play, of course, but you can also check what racial abilities give to each class as benefits:

Goblin Rogue
A Goblin gets a Rocket Jump (shared with a rocket barrage), can summon a mobile bank, gets the best discount at any vendor, a bonus to Alchemy and a 1% increase in attack speed.

This benefits all types of Rogues, and with the exception of the Alchemy bonus (for which you actually have to take the Alchemy profession) there's no "wasted ability".

Orc Shaman
An Orc can go Berserk (increasing Attack Power and Spellpower), gets bonus Expertise when fighting with Axes and Fist Weapons, Stun effects last 15% shorter, and pets get 5% increased damage.

The resistance to Stun is useful in PvP, or while leveling, but loses a lot of its shine in dungeons or raids at max level. Berserk benefits all types of Shaman, while the Expertise bonus only really benefits Enhancement Shamans (melee types).

The 5% bonus on Pet Damage is still under debate; since patch 3.1 it also affects Shaman pets, but today the racial ability specifies it only works on Warlock, Hunter and Death Knight pets. I am not sure whether it would benefit a Shaman, in other words.

Conclusion

Goblin Rogues benefit more from their racial abilities (especially when they are alchemists), while Orc Shamans get full benefits only if they are specifically Enhancement Shamans. This means that if you decided to try out Elemental or Restoration, you will lose the benefit of half your racial abilities.

If you are focusing on getting the most out of your character, Goblin Rogue seems to be the way to go. If the Orc's Command ability affects Shaman pets, then the Enhancement Shaman is a close second.

If you are focusing on versatility, the Shaman class wins because it can also heal, while the Rogue can only perform a DPS role.

If you are focusing on having a good time, simply pick which one appeals to you the most.