I always do Kasumi's loyalty quest so I can pick up the Locust submachine gun as early as possible. My Shepard is a vanguard, and the SMG is about as heavy as she can roll, and Locust is the best, plain and simple.
Later on Shepard gets advanced weapon training, and I always choose sniper rifles because sniping is just so much damn fun.
As for heavy weapons, the Cain is amazing- launch a nuclear warhead!- but I tend to have the Arc Projector with me at all times. It's a chain lightning gun, and it's great for taking down heavy mechs.