The Assault Rifle "Falcon" is imo pretty much the best weapon around. Maybe not the best for everyone, but it does a lot of work. It doesn't hit as hard as say a sniper rifle or shotgun, but its area of effect and has a healthy firing speed. It can also easily bounce around corners/cover. and is accurate at medium distance ( and it explodes so close counts). The hits also tend to "stagger" enemies briefly making follow up hits easy. I recommend modding it for clip size and damage.
As a vanguard I also liked chargeable weapons like hand held arc projector, Graal Spike thingiy or the Geth Plasma shotgun. Since you can use the invincibility of biotic charge to charge them up. Not so great for hiding behind cover, but if you're just bouncing around and using charge to keep your shields up they got excellent damage per shot. You can also use most abilities while charging a shot too so it doesn't limit your ability to use pull etc.They do tend to need to be reloaded more often than I'd like in bigger battle though.
As for armor. Inferno armor is good when starting out, but I prefer the blood dragon armor, but there's a full set of each" type" so If you want +50% tech damage you can eventually get it. If you want like 35% weapon dmg and 15% head shot dmg that's an option too. So at the end of the game the full suits of armor tend to pale in comparison to an individual set focused on what you want.
Armor is class dependent. For Soldier I was relying on the misc. pieces that gave 10% to weapon damage since I was using Marksman and Adrenaline Rush to blow stuff up and didn't need the bonus health/shields, skill damage, or CDR.
For Sniper rifle it's entirely debatable on class. Maybe the Infiltrator(?) can make the auto-rifles work better, but for me who was using it to 1-shot at long range Then Black Widow > Widow > Mantis for hard burst.
I didn't use SMG/Pistols, but I figure the Spectre pistol is probably best - or maybe the Arc Pistol.. I had the Eagle on allies.
Shotgun - Spectre one hands down. I say this because I wasn't sure in % damage can exceed the bars confines (which means extended barrel pushes the Krogan Claymore beyond max). Wraith is the Claymore with two shots in the barrel and slightly less damage. It was 1-shotting everything for me so I can't see much reason to go with the oen with less shots.
Battle Rifle - I used the Revenant. It just beats most Rifles in stats and fires a constant stream. I used it with Marksman so accuracy wasn't much importance.
Oddly, the pistol Predator that you start the game with is one of the strongest weapons in both sustained and burst damage potential, plus it's very accurate, has almost no recoil, and holds a good deal of amm... Uh, heat sinks.