The commonest problems at the start are a stiff wrist, pushing the string with the finger joint, and using the whole arm. Once these become habits they limit speed badly later on.
The more natural approach is for the arm to move the wrist and the wrist to move the fingers, passing force from shoulder and arm to the fingertip. Stay relaxed at the moment of contact and return to a loose state immediately after the stroke.
The contact point should stay relatively constant, usually at a fixed proportion of the vibrating length. Letting it drift makes the tone alternate between bright and dull and affects intonation as well.
Apply force perpendicular to the string where possible. Pushing at an angle gives a thin tone and, over time, can cause discomfort in the finger joints. When pressing or sliding, pay attention to the support from the palm and the coordination of the wrist.
There is no single correct hand shape, but relaxed, stable and repeatable are the shared criteria. Practise slowly to confirm the motion, then build speed gradually.