Adepts are relatively worthless against Mobs with shields. I'd avoid Adept because of how dependant they are on stripping enemy defences. Pick up Armor Piercing as your bonus power, it's better than Incendiary ammo for Armor damage. Don't bother getting Squad Ammo Powers and focus on maxing your own DPS, as you're likely not running Weapon-focused squadmates as a Soldier. Avoid the Revenant when the time comes, pick up the Widow instead.

I'd avoid using weapons that require you to peek for long periods of time, instead use slower, high power weapons. Soldier can be pretty good, but you need good positioning and proper threat management to be effective. Vanguard can also get free shields with Charge, but exercise restraint when doing so (countless hours of ME3 Multiplayer has shown how quickly a brainless Vanguard player can get killed).

Sentinel gets free shield recharge with Tech Armor and has some good synergy with all companions.

Infiltrator is good for cloak and getting free shots on enemies and repositioning if you get caught in a tight spot.