In the Destiny 2 beta, there are three exotic weapons. When the Homecoming mission starts, kill the first few Cabal and make your way to a hallway full of refugees. Here, Lord Shaxx will let you borrow a big, golden weapon from his own personal stash. Run up and claim your first exotic.
The guns are different depending on the class you choose.
Riskrunner, energy submachine gun - Warlock
The Warlock’s Riskrunner puts a constant stream of electricity flowing through your fingertips. On the surface, it is a completely ordinary submachine gun, one of Destiny 2’s new weapon classes. However, when its exotic perk activates, this beast can fire constantly, chaining lightning between enemies.
If you take any kind of arc damage while Riskrunner is equipped, it will become charged due to Arc Conductor, its exotic perk. In its charged state, you will take less arc damage and all of your shots have a chance to chain lightning between enemies while returning bullets to the magazine. Effectively, activating Arc Conductor allows you to fire endlessly into your enemies. As long as your shots are true, you will never have to reload.
Sweet Business, kinetic auto rifle - Titan
To call the Titan’s Sweet Business an auto rifle is to criminally underrate its speed and ridiculousness. This thing is a mini gun, and that comes with all of the perks and baggage that you think it should. It starts off firing very slowly before picking up a tremendous amount of speed. It has a 99-shot magazine, is very accurate when firing from the hip and will fill the magazine with white ammo you pick up while at full speed. This aids its quality of life, allowing you to have a decent amount of time at full speed before having to reload.
If you are able to hold down the trigger and stay accurate, Sweet Business can melt the health bar of any boss or enemy you come across. However, if you have to take short bursts, Sweet Business will not be the greatest ally. Each bullet does low damage, so getting a few shots in before hiding will not be helpful, especially compared to many of the legendary scout rifles and hand cannons.
Sunshot, energy hand cannon - Hunter
The Sunshot is perhaps the most situationally balanced of the three exotics. Whether you are in PvE or PvP, at close or long range, Sunshot is powerful and easy to use. Point, shoot, kill. Nothing as complicated as Sweet Business or Riskrunner.
However, this simplicity comes with the negatives of relatively bland perks. The exotic perk is Sunburn, which makes Sunshot shoot explosive bullets and highlight enemies it damages. Additionally, when enemies killed with Sunshot explode, dealing damage around them. These perks feel great to use but are not terribly noticeable. If you aren't paying attention, Sunshot will just seem like a fluidly designed hand cannon, rather than a situational exotic with objectives to be met.