For rabbits in general, it's not so much about the species, but the breed. Normally you'll want breed 5 (S/S), because Dodge is one of their key abilities, and it lets you avoid two attacks when you go first. I think all but the Elfin Rabbit have S/S as a possibility, so any species but that one will work. Unfortunately, in many cases rabbits have so many available breeds that it's a pain to find the right one. However, the spring rabbit, which many pet collectors already have, is always breed 5. It starts Uncommon, but if you've got one of those and a spare battle-stone, you won't have to hunt for anything.
As Stencil pointed out, though, the grasslands cottontail is a special case. It has different base stats, doing more damage at the cost of speed. If you get an S/S breed of that it will hit harder and still be faster than most pets. The major exception is Sludgy, the Thundering Pandaren Spirit's ooze, which is faster than an S/S grasslands cottontail, but not S/S rabbits of other species.
Outside of battle stats, in my opinion the best rabbit is the tolai hare pup. It's so teeny!