Strictly PVP perspective here.
Autorifles: Vanquisher model for sure. Few ways to approach it, as stated the vendor roll is actually pretty good. Field scout or fast reload on kill is what you want, then range/stability past that. Stitch in those headshots. Blah blah Suros Regime, etc. Still really good.
Scouts: Stability Perk (Rodeo or Zen Moment or Perfect Balance) and/or a reload perk, plus Third Eye so you can watch your flank while scoped in plinking at people. Oh wait, that's Fang of Ir Yut! Seriously, if you wanna run a non-MIDA scout in PVP this gun is amazing, with Perfect Balance it's a goddamn laser.
Pulse rifles: Reserving judgement until the patch. Had some decent luck with the vendor Three Little Words damage model though. Keep an eye on Red Death, if it goes back to being a two-burst kill gun it will do very well.
Hand Cannons: Any of the exotics. Seriously, they're all insane - I'm partial to Thorn as it's a little more versatile than TLW, and I play on XB1 so Hawkmoon isn't a thing. Yet. Barring that, a Red Hand IX with Send It or Perfect Balance, Third Eye (notice a pattern? ADS radar is crazy good.) and Rangefinder for long distance headshots. Technically Word of Crota has a slightly faster TTK if you land all headshots, but that's going to be a rarity - with the Red Hand damage model you can go 1 bodyshot 2 headshots and be fine. Really any of the faction hand cannons except for The Devil You Don't are fine, they're all basically the same aside from ammo count.
Sniper Rifles: Prudence II with Ambush scope, Unflinching, Perfect Balance, and whatever last perk you want. Fastest followup shots in the game, and just as stable as Praedyth's Revenge. Praedyth's is crazy good though, mostly because it lets you cap stability and still run field scout. Total judgement call here, unflinching vs field scout. Efrideet's Spear with Ambush Scope/Unflinching/AP rounds/Final Round for one-shot wallhack tricks is fun too, but for traditional sniping, followup shots with it are much slower than something like Praedyth's.
Fusion Rifles: I have a Perun's Fire with ORS1 scope/Hipfire/Send It/Feeding Frenzy. It's nasty. Charge rate is high enough without the accelerated coils boost that running send it for faster projectile speed becomes a good plan. Don't use fusions much, but when I do it's this or Plan C, Hipfire is such a good perk for tightened blast spread.
Shotguns: Mixed feelings here. The best perks are any of the range boosting ammo types/hammerforged/shot package, the tricky bit becomes balancing out ROF and Impact. I have a Judgement VI shotty with what amounts to max range on a purple shotgun and grenadier/shot package, but incredibly low ROF. I very rarely lose 1v1 heads-up shotgun engagements with it due to the crazy range, but it gets dicey when I have to do followup shots because of the low ROF. My personal 'perfect' shotgun for this archetype would be Field Choke/Kneepads/Hammerforged/Shot Package on a The Crash or Hide and Seek-42 (or old Comedian) - good balance of ROF and range. As mentioned, the vendor Secret Handshake is fantastic.
Rocket Launchers: Base 2 rockets in the tube launcher with high velocity, high blast radius, Grenades and Horseshoes, Clown Cartridge or Spray and Play. Most of the maps are small enough that Tracking isn't as much of a concern as being able to hipfire shots down a hallway or through doorways and have the proximity sensor do the work for you, hence large blast radius being important. I have a Radegast's Fury with Field Scout and GaH, and while the ROF is sloooow (delay between shots can feel like years) it's been serving me well. I didn't manage to get Clown Cartridge on it, but that'd be the optimal layout. If you have a launcher with 2 in the tube base, it's not going to be velocity or blast radius capped - look for perks to offset that weakness (Javelin and Heavy Payload, respectively) and ammo types to do the same. Truth is head and shoulders the best PVP launcher because you can spec it for high velocity/blast radius/proximity and still do insane cross-map tracking shots.
Machine Guns: Honestly, anything with Field Scout. I'm partial to the Deviant Gravity-A style and AOO/Jolder's style because they're a little easier to control, but plenty of players swear by Corrective Measure. Your AOO roll, as mentioned, is pretty awesome - Crowd Control for PVP lets you 1v2 pretty easily, and Rodeo is a great perk. I think my perfect roll would be a Jolder's with Smart Drift Control, Rangefinder or Counterbalance, Field Scout, and Surplus.
Honorable mention to the Vex Mythoclast for being an insanely good PVP primary.