The primary weapon is your main source of damage and it is the most frequently used of all of your weapons.
The Best Special Weapon
The Best Heavy Weapon
All Destiny Guides
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.
auluftwaffles.com, short video game guides 
Heres another auto rifle test after hot fix 1.0.2.2 on 10/14/2014. Bungie changed our auto rifles a little bit.
Base damage was decreased by %2, which is negligible in PVP.
Precision damage multiplier was decreased from 1.5 to 1.25, we see a definite decrease in head shot damage but nothing too dramatic.
There was also a decrease in stability, but I saw no real difference while playing.
In the video the Suros Regime, Silvered Hushwind-D, Shingen-E and Galahad-E are tested.
The best auto rifles for PVP IMO are listed above in that order.
The SUROS Refime is the best Auto Rifle out there. Check out the video below towards the end for the suros. There are a series of these videos testing out different auto rifles in PVP.