The primary weapon is your main source of damage and it is the most frequently used of all of your weapons.
The Best Primary Weapon PvP The Crucible Destiny
In the primary weapon slot in Destiny the easiest to use are auto rifles. When you select which auto rifle to use in the Crucible you want a weapon that can get you headshots easily and do a lot of critical damage. Hence you want a low recoil, high impact auto rifle. When you are in an engagement you always want to shoot at the head of your opponents since you do a lot more damage that way.
If you can get headshots easily with hand canons they are also very good. Note that any hand canon with less than 10 shots between reloads is probably not worth it since you would have to reload too often. Right now pulse and scout rifles are the worst primary weapons due to the map layout favoring close quarters.