you'll unlock new skills as you level up your base skills in the squad menu. you can highlight future skills to plan what you want to master in. and once you become a spectre, and complete the rogue mission, you have the choice of becoming a new class.
what are you starting off as?
also, if you're playing it shooter style like halo, it's going to be a mess. just focus on getting your target locked on and firing away. you don't have to be accurate to get hits on enemies, that's the rpgish nature of the gameplay. use all your biotics if you've got 'em too.