Barbas is unkillable once you finish the first part of the Daedric quest associated with him. Some people find his voice annoying but you don't have to speak with him unless you are doing specific parts of the quest. While the barking can also be annoying, the game doesn't count it as sound for detection so it wont compromise your stealthplay. I find Barbas's most annoying characteristic to be his defective pathing AI. For whatever reason he wants to stand on the exact same spot you are standing instead of besides you like the pathing AI for most followers. This results in him constantly pushing you, and more than one player character, including one of mine, has been shoved off a cliff or other high ledge by him to their death. Even with that comical instance aside, he can also ruin stealth Archery attacks by shoving you as you release your arrow.
If you like dog followers and hate the idea that yours can die (and most dogs eventually will die when you are at high levels) then Barbas may be a suitable animal follower for you, but I found him to be a novelty that lost its charm over time.
Banning 's the dog out front of Markarth who you can buy for 500septims. He barks a bit less than barbas too but he don't have that wise guy voice, dope voice actor.
Banning is not a dog. He's a dog trainer at the Markarth Stables. He will sell you a dog named Vigilance though, and Vigilance has the highest level cap of any dog in the game (50). Even though you "buy" him from Banning, you should treat him as a hireling follower as he will return to Markarth Stables if you dismiss him or he leaves when you make him wait in a spot too long. The only way to get him back is to purchase him from Banning again.