Two Anub idols should be the go-to team for all Pandaria tamers, not necessary fastest though.
For Anubs, do not use Demolish unless the tamer have Beast AND they don't have elemental. Crush deals (414 - 70) * 0.7 ~= 240 dmg, Demolish does (592 - 70) * 0.4 ~= 209, both under Sandstorm. Higher miss chance also means less healing received.
Pets you may want to experiment with would be (Jade) Oozelings with 2-1-2 (can solo Nishi and heavily damage Water elemental, as well as being good opener on most others) and Onyxian whelp (huge power, low speed = tail sweep is good, abuse ai patterns to make use of Lift-off and Healing flame, resilient to so many Flying attacks and trainers don't use human or undead pets so weaknesses are irrelevant).
For my Pandaria tamer sweep, I use Anub, Onyxian and Ooze for all tamers, swapping one (depending on trainer I'm facing) for carry. Exception is Dread Waste trainer, where the team works fine, but Flying pet on start makes it so much quicker against crab, and Thundering elemental, where you need 300+ speed Rabbit for first and third of his pets.