I've tried to start playing D&D a few times, but it's pretty hard to get started without a real group. Anyone willing to introduce me to the game in a proper way?

Well if all else fails you can always go to the thursday meeting sometime.

I usually play sentinel with Garus and Wrex because they make up for lack of combat and on hard I combine my Overload and Sabatage with Garus, my suggestion is to have Tech and Biotics in your party.