There is one significant difference between MK (Mouse & Keyboard) and Controllers:
Considering the lack of simultaneous accessibility, limited turn space, Controllers are usually inferior compared to MK, especially in fps.
Well, that doesn't apply for Black Ops 3, believe it or not, the strong Aim Assists in this game completely reverses that.
Once Controller players hit the first shot, their following shots will never miss the target, whereas MK players can still flinch, aim away and lose the gunfight. When you ads with a gamepad, the Aim Assist kicks in and starts working like a magnet, it automatically snaps on the enemy. Even if you actually aimed bad, the AA corrects everything; it has a very big threshold and does basically 90% of the actual Aiming for you!


Note:
Just for the record, Black Ops 3 does not have Aim Assist (AA) in multiplayer, it´s called Target Assist (TA) instead. Ironically TA is stronger than every Silent Aim. When people are speking of AA they usually mean TA.

It doesn't matter, use any (supported) Controller of your choice.

BO3 natively supported controllers include:

• Those with XInput (all Microsoft Controllers; Xbox One, 360 Controller)
  
• PS4 Controller

If you want to play with another Controller (e.g. PS3 Controller) you will have to use an XInput Wrapper.

The most important attachment is stock, as it increases AA when you are moving

You have your biggest advantage in close to midrange fights, where you can take advantage of your artificial aiming (:D) to relentlessly melt down MK players.
Always move your Left Thumb-Stick to left and right during gunfights; that will give you more AA and makes yourself harder to hit
Play smart and aggressive; always remember that you only need to look in the approximate direction of your enemy and press L1/2 + R1/2 to let the AA do all the work for you.

It is generally advisable to play with a lower sensitivity (< 1.50), because you´ll receive more AA.
The best sense is the one you feel comfortable with and don´t need to warm up too long for.

Most gamepad users play with "Stick and Move", that maps jumping on R3.

When people call you names like "controller ♥♥♥♥♥♥" they actually intend to praise your skill playing with a primitive input device, so be friendly as well and reply "<3"