What DLC's do you have....... Citadel, Omega, Leviathan, From Ashes? What difficulty level (Damage Reduction by Armor depends on the difficulty level, -50 Damage per bullet on insanity as the maximum).
Weapons....it is always a matter of your prefered playstyle and the combination with the weapons mods.
A game with no DLC's... I'd say (Sabre's too late in the game) Revenant, Mattock for quick fingers, Claymore, (Black) Widow, Javelin, Wraith, Paladin along incendiary ammo Explosive Burst Evolution, cryo squad ammo, a shredder mod and/or a barrel to increase the damage.
The Soldiers Adrenaline Rush increases weapons damage and the Vanguards Charge puts you into point blank range and he can increase shotgun damage, depending on the evolutionary ranks you choose.
AP Ammo is a nice Bonus Power, but less usefull as Soldier or Vanguard, as they already have Incendiary Ammo which provides more damage overall than AR could.
In general there are plenty of ways to deal with armor.
Powers, power combos like cryo and warp reduce the armor by 25/50 percent depending on the talent point you spent. Take Tali with you. Her Sabotage is a debuff that doubles the the tach damage the target recieves.... so it doubles your incinerate or overload for example.
Slow firing weapons deal more base damage, so piercing mods have less impact than high caliber mods that increase the damage.... except some DLCs combined these into one heavier modification.
If You have Citadel DLC, it's the Supressor including Pistol Magazine Upgrade and Piercing Mod or High Caliber Barrel. This thing ridicioulsy melts armor in single player on everything including Atlases and Banshees, as you can empty the full clip in under 3 seconds, if you have quick fingers. As a soldier you always should have a backup weapon and the vanguard charges or novas his way out or through trouble.
Early in the game you have access to the mattock and the Eviscerator (Grissom Academy right after Priority Palaven) The Mattock for The Soldier and the Eviscerator for the Vanguard.
Later I change the Mattock with the M7 Lancer and the Eviscerator with a Claymore or a Wraith. Though the Vanguard is more depending on power cooldown, I upgrade the Eviscerator/Wraith due to the low weight with a High Velocity Barrel V from DLC Omega.... more damage and piercing in a single mod without sacrificing too much cooldown. The Claymore is too heavy for that, so take shredder mod and high caliber barrel here.... the base damage is high enough that you still melt armor.
The lancer combines acceptable damage output alongside a high rate of fire. A Mag upgrade is a must.
Snipers for the Soldier... take what you like most..... Javelin, Black/Widow.