Not a lot of walls to perform right hand advantage with in Story Mode.
Soldier: A very adaptive playstyle that offers high weapon damage boosts. Use ammo powers to your advantage to deal with most defenses, and use Concussive Shot to create Tech bursts, Fire explosions, and Cryo Explosions with ammo powers. The Soldier is good for all situations, but not so good for crowd controlling as Frag Grenades are finite and on harder difficulties grenades do not replenish as often. Make sure to spec for a more survivable Soldier.
Adept: Biotic Explosion expert. Offers very damaging biotic explosions that contributes to crowd control. The best at chipping away armor and barriers, but poor against shields, but that won't be much of a problem. It would be best that you don't bring tech squadmates too often as their powers may override your priming biotic powers(mainly Warp).
Vanguard: If you want to play the close-range style, you're gonna have to learn to Nova-cancel a lot, and learn when to Biotic Charge and when to not. Use Incendiary Ammo to create some Fire Explosions with Biotic Charge and Shockwave. The Vanguard is good at crowd control, but is not that good at it if Nova is not used carefully or at all.
Sentinel: Survivable and possesses the necessary powers to crowd control and debuff enemies. A Sentinel's best powers are Tech Armor, Lift Grenades, Cryo Blast, Warp, and Overload. Can create strong Biotic Explosions with Warp and Throw, Tech Bursts with Overload and Warp.
Engineer: Very good at crowd control with Overload, Combat Drone, and Sentry Turret. Great debuff with Cryo Blast. Incinerate and Overload will be your two highly used powers, if not. Certain enemies will cause a lot of problems to you like Banshees and Phantoms since they will block your powers most of the time since most your powers are projectile powers.
Infiltrator: Very survivable, but also a very high damage dealer with weapons and powers when used with Tactical Cloak. Use Sticky Grenades for dealing quick massive damage(Sticky Grenades prime the sticky'd target with the ammo type currently used before detonating(I believe your ammo powers are Disruptor and Cryo)which will cause a cryo explosion or a tech burst depending on the ammo type. Also, upon sticking onto the target, it will do 50% of the damage of the currently held weapon). Create Tech Bursts with Sabotage + Incinerate, or Disruptor Ammo + Incinerate. The Infiltrator is not so good at crowd controlling.