You'll be definitely singing a different tune about not needing skills once you hit Hardcore mode. My suggestion is a Soldier with Barrier (you will NEED barrier to survive as a tank), or an Adept with either Electronics (shields = love) or Shotgun or Assault Rifle. Shotgun will help you early on, but you'll score much more damage at range with a Spectre X assault rifle with damage and heat upgrades. Also, if going Adept (which really shines in Hardcore and Insane), be absolutely sure to pick the subclass that upgrades Singularity. Nothing sucks worse than stopping three charging Krogans only to find out that you cant harm them until the effect wears off.
Supplement your party with both Garrus (electronics and sniper rifle), Wrex (OMG TANK RUSH KEKEKEKE), or Liara (biotics in Hardcore = essential).