Well, I'm not sure if you're aware of the hand cannon problem, bu they're pretty broken right now. The only ones worth using are ones with very high range. In my experience, the Eyasluna with Rifled Barrel (Increased range, slower reload) is the best primary for PvP. It drops randomly from crucible and from The True Meaning of War, the Shaxx weekly bounties. The perks on it matter much less than an increasing range in the middle, but things like Hidden Hand, Rangefinder, and Outlaw are probably the best.
The Hawksaw and Suros PDX pulse rifles are really good as well, really the only perks you want are stability increasing ones, except the PDX can roll with full auto if that's what you're into.
Otherwise, the MIDA is back and better than ever (not sure if you were around for that), and TLW is used a lot. The Universal Remote has also seen a lot of use recently since you can always have shotgun ammo.
As far as the specials go, fusions are still terrible. So that leaves snipers and shotguns.
For snipers, high impact is the meta (1000 Yard Stare, Y-09 Longbow Synthesis, LDR 5001). Aim assist has been a hot topic recently, and the Longbow has the most of it, so that's the one you're looking for. Perks are basically just Unflinching and Hidden Hand for PvP. LDR drops from Vanguard packages, Longbow from Crucible, and 1KYS from engrams and such.
Shotguns are pretty boring, it's still just the highest impact with range increasing perks and hopefully rangefinder on it as well.