The gun with the fastest bullets and firing rate would probably be the Blitz Needle, Plague Needle or Volcanic Pepperbox.
The gun with the fastest movement speed would probably be the Argent Peacemaker or Sentenza.
The gun with the fastest charge time would be Biohazard or Neutraliser.
The gun with the most damage per second would be debatable, since I don't know what family type you would be looking for... but it would probably be one of the 5* Autogun lines, if all the bullets hit.
Please be more precise as to what you're looking for. We're still not psychic.
What do you mean by "fast"? Do you mean "most damage per second"? Do you mean "most projectiles per second"? Do you mean that you're able to move quickly while firing? Do you mean "fastest charging"?
Assuming that your question is sincere, we could help you much better if we knew *why* you wanted such a fast gun.
Another, even bigger question is: Why do you want a 2-star gun? You don't want to get a good 2-star gun, only to realize later that it leads to a useless 5-star gun. I recommend that you select the 5-star guns that you like, and then select the 2-star guns that get you to them.