Car driving question?

Have a question about stopping the car and pulling away. When I'm at traffic lights that are about to turn green or I'm stopping momentarily at a junction to wait for a car, I leave the handbrake down, I've been told to do that. When I'm pulling away with handbrake up I feel the bite easily because with the handbrake up I can feel the car trying to lurch forward, I drop clutch a fraction and then I'm at the bite. With the handbrake down I obviously don't get this lurch so I tend to go past the bite and stall. Any tips on finding the bite with handbrake down? Also if I've stopped the car for a sec am I supposed to take my right foot off the brake before I find the bite with my left foot, or keep right foot on the brake until I find the bite, then move right off brake and move it to accelerator when I want to move off, I'm scared of rolling.