The bar shouldn't make more than a small arc from the chest upwards. A bit of a rear arc is "ok". Though also the form depends if you're doing powerlifting style or not.
When the bar's at the bottom you should explode with your feet as well - you get a lot of power from your legs when benching. Before starting be sure that you lock your core down, lock the shoulder blades back together, engage the lats as well, and keep chest up and don't let shoulders roll forwards. Make sure you push with your feet on your heals - this will stop hyperextending your back they should be perpendicular to the floor, and keep a strong arch and again - strong core! Stare at the ceiling, not at the bar.
Get a spotter, you don't want to unrack with bent arms. KEep your wrists locked, and not bent. I prefer a grip of just more than shoulder width apart. Don't lift your head, but don't push with it either. Elbows shouldn't be perpendicular nor parallel to the upper body, but in between.
Just to recap:
Core locked.
Strong arch.
Shoulder blades together.
Locked wrists.
Heals on the floor.
Straight arms.
Chest up.
Lock core.
Push with legs.
Core tight.
Don't have your elbows too wide or too narrow.
Don't roll shoulders forwards.
Core tight.